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social science
introduction to logic

A Concise Introduction to Logic 13th edition Patrick J. Hurley, Lori Watson - Solutions

H ≡ ∼ G…………………………..(G ∙ H) ∨ (∼G ∙ ∼ H)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or inconsistent. First, determine whether the pairs of propositions are
∼ A ≡ X…………………………..(X ∙ ∼ A) ∨ (A ∙ ∼ X)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or inconsistent. First, determine whether the pairs of propositions are logically
R ∨ ∼S……………………………S ∙ ∼ RUse truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or inconsistent. First, determine whether the pairs of propositions are logically equivalent or
∼K ⊃ L…………………………..K ⊃ ∼ LUse truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or inconsistent. First, determine whether the pairs of propositions are logically equivalent or
∼K ⊃ L…………………………..K ⊃ ∼ LUse truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or inconsistent. First, determine whether the pairs of propositions are logically equivalent or
F ∙ M……………………………..∼(F ∨ M)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or inconsistent. First, determine whether the pairs of propositions are logically equivalent or
∼D ∨ B…………………………..∼(D ∙ B)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or inconsistent. First, determine whether the pairs of propositions are logically equivalent or
[(F ∨ E) ∙ (G ∨ H)] ≡ [(G ∙ E) ∨ (F ∙ H)]Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
{[(G ∙ N) ⊃ H] ∙ [(G ⊃ H) ⊃ P]} ⊃ (N ⊃ P )Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
[U ∙ (T ∨ S)] ≡ [(T ∨ ∼ U) ∙ (S ∨ U)]Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
[(H ⊃ N) ∙ (T ⊃ N)] ⊃ [(H ∨ T) ⊃ N]Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
[(Q ⊃ P) ∙ (∼Q ⊃ R)] ∙ ∼ (P ∨ R)Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
[G ⊃ (N ⊃ ∼G)] ∙ [(N ≡ G) ∙ (N ∨ G)]Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
[X ⊃ (R ⊃ F)] ≡ [(X ⊃ R) ⊃ F ]Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
[(C ⊃ D) ∙∼ C] ⊃ ∼ DUse truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
[(Z ⊃ X) ∙ (X ∨ Z)] ⊃ XUse truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
(M ⊃ P) ∨ ∼ (P ⊃ M)Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
(M ⊃ P) ∨ ∼ (P ⊃ M)Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
(∼K ⊃ H) ≡ ∼(H ∨ K)Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
[(E ⊃ F) ⊃ F] ⊃ EUse truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
(S ⊃ R) ∙ (S ∙ ∼ R)Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
(G ⊃ G) ⊃ GUse truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
N ⊃ (N ⊃ N)Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.
Create three simple propositions that you know to be true, and three simple propositions that you know to be false. Then select letters to represent these six simple propositions, and combine these letters in various ways to produce five compound propositions. Finally, use the rules for the logical
[Q ⊃ (A ∨ P)] ≡ [(Q ⊃ B) ⊃ Y]When possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
[(Z ⊃ P) ⊃ P] ⊃ PWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
∼(Q ∙ Y) ≡ ∼(Q ∨ A)When possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
∼(P ⊃ Y) ∨ (Z ⊃ Q)When possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
(Q ⊃ B) ⊃ (A ⊃ Y)When possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
(P ⊃ A) ≡ (Q ⊃ B)When possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
(P ⊃ A) ⊃ ZWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
P ≡ ∼ PWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
A ⊃ PWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
Z ⊃ QWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
P ⊃ BWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
Q ∙ AWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
Q ∙ YWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
Q ∨ ZWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
A ∨ PWhen possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write “undetermined.”
(Z ⊃ C) ⊃ {[(∼X ⊃ B) ⊃ (C ⊃ Y)] ≡ [(Z ⊃ X) ⊃ (∼Y ∼ Z)]}Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼{∼[(C ∨ ∼B) ∙ (Z ∨ ∼ A)] ∙ ∼ [∼ (B ∨ Y) ∙ (∼X ∨ Z)]}Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
[(B ∙ ∼C) ∨ (X ∙ ∼Y)] ⊃ ∼ [(Y ∙ ∼ X) ∨ (A ∙ ∼ Z)]Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼[(A ≡ X) ∨ (Z ≡ Y)] ∨ [(∼ Y ⊃ B) ∙ (Z ⊃ C)]Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
[(∼X ∨ Z) ⊃ (∼C ∨ B)] ∙ [(∼X ∙ A) ⊃ (∼Y ∙ Z)]Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
(X ⊃ Z) ⊃ [(B ≡ ∼ X) ∙ ∼ (C ∨ ∼ A)]Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼[∼ (X ⊃ C) ≡ ∼ (B ⊃ Z )]Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼[(B ∨ ∼C) ⊃ (X ∨ ∼Z)]Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼(A ∙ ∼C) ⊃ (∼X ⊃ B)Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
(C ≡ ∼A) ∨ (Y ≡ Z)Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
(Y ⊃ C) ∙ ∼ (B ⊃ ∼ X)Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼(X ∨ ∼ B) ∙ (∼Y ∨ A)Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
(A ∙ Y) ∨ (∼Z ∙ C)Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
A ⊃ ∼(Z ∨ ∼ Y )Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼B ∨ (Y ⊃ A)Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼ (A ∙ ∼ Z )Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼C ≡ ZDetermine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
B ≡ YDetermine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼X ⊃ ZDetermine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
Y ⊃ ∼ADetermine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
B ⊃ ∼ZDetermine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
∼C ∨ ZDetermine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
X ∨ ∼YDetermine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
B ∙ ∼ YDetermine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.
Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.A ∙ X
Custer was killed by the Indians, and Lincoln wrote the Gettysburg Address only if either Washington was assassinated or Julius Caesar conquered America.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to
It is not the case that Custer was killed by the Indians unless both Nixon resigned the presidency and Edison invented the telephone.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth
Both Hitler ran the Third Reich and Lindbergh crossed the Atlantic if neither Einstein discovered aspirin nor France bombed Pearl Harbor.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the
Lincoln’s having written the Gettysburg Address is a sufficient condition for Julius Caesar’s having conquered America if and only if Washington’s being assassinated is a necessary condition for Custer’s having been killed by the Indians.Write the following compound statements in symbolic
Lincoln’s having written the Gettysburg Address is a sufficient condition for Julius Caesar’s having conquered America if and only if Washington’s being assassinated is a necessary condition for Custer’s having been killed by the Indians.Write the following compound statements in symbolic
Either Lindbergh crossed the Atlantic and Edison invented the telephone or both Nixon resigned the presidency and it is false that Edison invented the telephone.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple
If Hitler ran the Third Reich, then either Custer was killed by the Indians or Einstein discovered aspirin.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound
It is not the case that either Julius Caesar conquered America or Washington was assassinated.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
Lincoln wrote the Gettysburg Address if and only if France bombed Pearl Harbor.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
Washington was assassinated only if Edison invented the telephone.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
Julius Caesar conquered America if Napoleon ruled France.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
Edison invented the telephone, or Custer was killed by the Indians.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
Hitler ran the Third Reich and Nixon did not resign the presidency.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
France bombed Pearl Harbor, or Lindbergh crossed the Atlantic.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
Nixon resigned the presidency and Lincoln wrote the Gettysburg Address.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
It is not the case that Hitler ran the Third Reich.Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
∼[(X ∨ T) ∙ (N ∨ F)] ∨ (K ⊃ L) Identify the main operator in the following propositions.
E ∙ [(F ⊃ A) ≡ (∼G ∨ H)]Identify the main operator in the following propositions.
[∼F ∨ (N ∙ U)] ≡ ∼HIdentify the main operator in the following propositions.
∼[(S ∨ L) ∙ M] ⊃ (C ∨ N)Identify the main operator in the following propositions.
∼[(P ∙ ∼R) ⊃ (∼E ∨ F)]Identify the main operator in the following propositions.
(M ∙ B) ∨ ∼[E ≡ ∼(C ∨ I)]Identify the main operator in the following propositions.
∼(K ∙ ∼O) ≡ ∼(R ∨ ∼B)Identify the main operator in the following propositions.
∼[P ∙ (S ≡ K)]Identify the main operator in the following propositions.
(G ∙ ∼ P) ⊃ (H ∨ ∼ W)Identify the main operator in the following propositions.
∼(A ∨ M ) ∙ ∼ (C ⊃ E )Identify the main operator in the following propositions.
Construct compound propositions involving at least three simple propositions about the following topics. Then, symbolize your propositions as per Parts I and II of this exercise.1. Political figures2. NFL teams3. Corporations4. Brands of automobiles5. Music or film celebritiesPart I From This
(R ≡ S • T ) ⊃ ∼(∼W • ∼X )Determine which of the following are not well-formed formulas.
∼(F ∨ ∼G ) ⊃ [(A ≡ E ) • ∼H ]Determine which of the following are not well-formed formulas.
M(N ⊃ Q) ∨ (∼C • D)Determine which of the following are not well-formed formulas.
[(D • ∨ Q) ⊃ (P ∨ E )] ∨ [A ⊃ (• H )]Determine which of the following are not well-formed formulas.
∼D ∨ ∼[(P ⊃ Q) • (T ⊃ R)]Determine which of the following are not well-formed formulas.
(F ≡ ∼Q) • (A ⊃ E ∨ T )Determine which of the following are not well-formed formulas.
(B ⊃ ∼T ) ≡ ∼(∼C ⊃ U )Determine which of the following are not well-formed formulas.
(E ∼F ) ∨ (W ≡ X )Determine which of the following are not well-formed formulas.
∼(K ∨ L) • (⊃ G ∨ H )Determine which of the following are not well-formed formulas.

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