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social science
introduction to logic

Questions and Answers of Introduction To Logic

Q ⊃ ∼ (K ∨ F)………………….(K ∙ Q) ∨ (F ∙ Q)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory,
Z ∙ (C ≡ P)……………………….C ≡ (Z ∙ ∼ P)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent,
H ∙ (K ∨ J)……………………….(J ∙ H) ∨ (H ∙ K)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory,
R ∙ (Q ∨ S)……………………...(S ∨ R) ∙ (Q ∨ R)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory,
R ∙ (Q ∨ S)……………………...(S ∨ R) ∙ (Q ∨ R)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory,
G ∙ (E ∨ P)………………………∼ (G ∙ E) ∙ ∼ (G ∙ P)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent,
G ∙ (E ∨ P)………………………∼ (G ∙ E) ∙ ∼ (G ∙ P)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent,
W ≡ (B ∙ T)………………………W ∙ (T ⊃ ∼ B)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory,
M ⊃ (K ⊃ P)………………………(K ∙ M) ⊃ PUse truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or
N ∙ (A ∨ ∼E)……………………... ∼A ∙ (E ∨ ∼ N)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent,
(E ⊃ C) ⊃ L………………………E ⊃ (C ⊃ L)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or
H ≡ ∼ G…………………………..(G ∙ H) ∨ (∼G ∙ ∼ H)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent,
H ≡ ∼ G…………………………..(G ∙ H) ∨ (∼G ∙ ∼ H)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent,
∼ A ≡ X…………………………..(X ∙ ∼ A) ∨ (A ∙ ∼ X)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent,
R ∨ ∼S……………………………S ∙ ∼ RUse truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or
∼K ⊃ L…………………………..K ⊃ ∼ LUse truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or
∼K ⊃ L…………………………..K ⊃ ∼ LUse truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or
F ∙ M……………………………..∼(F ∨ M)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or
∼D ∨ B…………………………..∼(D ∙ B)Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent,
[(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
[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
[(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
∼(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
∼(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
(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
(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
(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
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
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
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
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
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
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
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
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
(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.
∼{∼[(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
[(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
∼[(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
[(∼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.
(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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
∼[(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.

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