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mathematics
a survey of mathematics with applications
Questions and Answers of
A Survey of Mathematics with Applications
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: jv k .. j
Construct a truth table for the statement.(p ∨ q) ∧ ~p
Construct a truth table for the statement.~p → (q ∧ r)
Use an Euler diagram to determine whether the syllogism is valid or invalid.Some skunks are tame.Pepé is a skunk.∴ Pepé is not tame.
Construct a truth table for the statement.(p ∨ ~q) ∧ r
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: Standard Forms of Arguments Law of
Construct a truth table for the statement.(~p ↔ q) → (~p ↔ ~q)
Use an Euler diagram to determine whether the syllogism is valid or invalid.Some mushrooms are poisonous.A morel is a mushroom.∴ A morel is poisonous.
Construct a truth table for the statement.(p ∧ ~q) ∨ r
Determine whether the argument is valid or invalid. You may compare the argument to a standard form,, or use a truth table.Data From argument to a standard form: e-f e if
Construct a truth table for the statement.(~p → q) ↔ (p → ~q)
Draw a switching circuit that represents the symbolic statement.p ∨ (~q ∧ ~r)
The Thunder will make the playoffs if and only if they win their last five games. Indicate whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate
Use an Euler diagram to determine whether the syllogism is valid or invalid.No Cyclones are Longhorns.Zendaya is not a Longhorn.∴ Zendaya is a Cyclone.
Construct a truth table for the statement.~p ∧ (q ∨ r)
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: a v b -a
Construct a truth table for the statement.(p ↔ q) ∨ p
Use an Euler diagram to determine whether the syllogism is valid or invalid.No lawn weeds are flowers.Sedge is not a flower.∴ Sedge is a lawn weed.
Construct a truth table for the statement.p ∨ (~q ∨ r)
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: a-b .. -b
Construct a truth table for the statement.p↔ (q ∨ p)
Use an Euler diagram to determine whether the syllogism is valid or invalid.All American Beauties are roses.No roses are daffodils.∴ No American Beauties are daffodils.
Construct a truth table for the statement.~(p ∨ ~q)
Construct a truth table for the statement.(p ↔ q) → p
Tony Stark makes an appearance in Spider Man and The Incredible Hulk. Indicate whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it
Use an Euler diagram to determine whether the syllogism is valid or invalid.No PCs are Macs.All Dells are PCs.∴ No Dells are Macs.
Construct a truth table for the statement.~(p ∧ ~q)
Construct a truth table for the statement.(p → q) ↔ p
(a) Write a symbolic statement that represents the circuit and(b) Construct a truth table to determine when the lightbulb will be on. That is, determine which switches must be open and which switches
Miles Davis did not play rap music. Indicate whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction,
Use an Euler diagram to determine whether the syllogism is valid or invalid.All dolphins are mammals.All mammals are vertebrates.∴ All dolphins are vertebrates.
Construct a truth table for the statement.~p ∧ ~q
Construct a truth table for the statement.~(p ↔ q)
Use an Euler diagram to determine whether the syllogism is valid or invalid.All yo-yos are toys.All Slinkies are toys.∴ All Slinkies are yo-yos.
A leap year has 366 days and a week has eight days if and only if an hour has 24 minutes.Determine the truth value of the statement.
Construct a truth table for the statement.p ∧ ~q
Construct a truth table for the statement.~p ↔ ~q
Fill in the blanks with an appropriate word, phrase, or symbol(s).Of the converse, inverse, and contrapositive, only the contrapositive of the conditional statement is to the _________ conditional
Use an Euler diagram to determine whether the syllogism is valid or invalid.All dogs are canines.Boomer is a canine.∴ Boomer is a dog.
Determine the truth value of the statement.2 + 6 = 8 or 7 - 12 = 5.
Construct a truth table for the statement.~p ∨ ~q
Construct a truth table for the statement.p → ~q
Fill in the blanks with an appropriate word, phrase, or symbol(s).Given the conditional statement p → q, the contrapositive of the conditional statement in symbolic form is _________.
John is taking Liberal Arts Mathematics during the fall semester. Indicate whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it is a
Construct a truth table for the statement.~p ∨ q
Construct a truth table for the statement. ~p → q
Fill in the blanks with an appropriate word, phrase, or symbol(s).Given the conditional statement p → q, the inverse of the conditional statement in symbolic form is _________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).a) The conditional is symbolized by → and is read “________.”b) The biconditional is symbolized by ↔ and is read “________
Construct a truth table for the statement.p ∨ ~p
Fill in the blanks with an appropriate word, phrase, or symbol(s).If the conditional statement referred to in Exercise 4 is not a tautology, then the argument is a(n) _____________ argument.Data From
Fill in the blanks with an appropriate word, phrase, or symbol(s).A conditional statement that is a tautology is known as a(n) _______ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).Given the conditional statement p → q, the converse of the conditional statement in symbolic form is _________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).a) The negation is symbolized by ~ and is read “________.”b) The conjunction is symbolized by ^ and is read “________.”c) The
Construct a truth table for the statement.p ∧ ~ p
Fill in the blanks with an appropriate word, phrase, or symbol(s).If the conditional statement referred to in Exercise 4 is a tautology, then the argument is a(n) _____________ argument.Data From
In Exercises 1–16, fill in the blanks with an appropriate word, phrase, or symbol(s).A compound statement that is always false is known as a(n) _______ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).The negation of the conditional statement ~(p → q) is equivalent to the following conjunction statement: _________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Words such as all, none (or no), and some are examples of ________.
Write each symbolic statement in words.p: Phobos is a moon of Mars.q: Callisto is a moon of Jupiter.r: Rosalind is a moon of Uranus.(~p ∧ r) ↔ ~q
Fill in the blanks with an appropriate word, phrase, or symbol(s).A truth table for a compound statement witha) One distinct simple statement will have _________ cases.b) Two distinct simple
Fill in the blanks with an appropriate word, phrase, or symbol(s).To determine the validity of an argument with two premises, construct a truth table of the form [(premise 1) ∧ (premise 2)] →
Fill in the blanks with an appropriate word, phrase, or symbol(s).A compound statement that is always true is known as a(n) _______ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).Two circuits are equivalent if they have equivalent _________ statements.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The conditional statement p → q is equivalent to the following disjunction statement: _________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A statement that consists of two or more simple statements is called a(n) ________ statement.
Fill in the blanks with an appropriate word, phrase, or symbol(s).If an Euler diagram can be drawn in a way in which the conclusion does not necessarily follow from the premises, the syllogistic
It is false that Rosalind is a moon of Uranus if and only if Callisto is not a moon of Jupiter.Write the statement in symbolic formp: Phobos is a moon of Mars.q: Callisto is a moon of Jupiter.r:
Fill in the blanks with an appropriate word, phrase, or symbol(s).The disjunction p ∨ q is false only when both p and q are _________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).An argument that is invalid is also known as a(n) _____________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).The biconditional statement p ↔ q is _______ only when p and q have the same truth value.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When a switch labeled as p is open, a switch labeled as P̅ is _________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).De Morgan’s laws state thata) ~(p ∧ q) is equivalent to _________, andb) ~(p ∨ q) is equivalent to _________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).If an Euler diagram can be drawn only in a way in which the conclusion necessarily follows from the premises, the syllogistic
Fill in the blanks with an appropriate word, phrase, or symbol(s).The conjunction p ∧ q is true only when both p and q are _________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When the conclusion of an argument does not necessarily follow from the given set of premises it is a(n) _____________ argument.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In the conditional statement p → q,a) The lower-case letter p represents the _______ .b) The lower-case letter q represents the
Fill in the blanks with an appropriate word, phrase, or symbol(s).A disjunction, ∨, is used to represent switches in a(n) _________ circuit.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Statements that have exactly the same truth values in the answer columns of their truth tables are called _________ statements.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The negation ~p will always have the _________ truth value of p.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When the conclusion of an argument necessarily follows from the given set of premises it is a(n) _____________ argument.
All diamonds are made of carbon.Write the negation of the statement.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The conditional statement p → q is _________ only when p is true and q is false.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A conjunction, ∧, is used to represent switches in a(n) _________ circuit.
Use inductive reasoning to predict the next three numbers in the pattern (or sequence).1, 3, 4, 7, 11, 18, 29, 47, . . .
The graph below shows the annual tuition, to the nearest hundred dollars, at Clarence Community College for the years 2015–2019.a) Assuming this trend continues, use the graph to predict the annual
Answer true or false. If false, give the reason.{AT&T, Verizon} ⊂ {Verizon, Sprint, T-Mobile, AT&T}
Construct a Venn diagram illustrating the following sets.U = {Costco, Dollar General, Marshall's, Nordstrom, H & M, Lowe's, Sprouts, Ross, Dollar Tree, Aldi, Urban Outfitters, Five Below, Ulta
U is the set of furniture stores.A is the set of furniture stores that sell mattresses.B is the set of furniture stores that sell outdoor furniture.C is the set of furniture stores that sell leather
U is the set of furniture stores.A is the set of furniture stores that sell mattresses.B is the set of furniture stores that sell outdoor furniture.C is the set of furniture stores that sell leather
Use Fig. to determine the sets.A ∪ C U A k a f b i, j h
The set of years in which Apple iPhone unit sales were less than 20 million.Use the following graph, created using Stat Crunch , which shows the worldwide sales of the Apple iPhone, in millions of
In Exercise, For set A = {a, b, c, d},a) List all the subsets of set A.b) State which of the subsets in part (a) are not proper subsets of set A.
Use the following table, which shows the amount of sugar, in grams (g), and caffeine, in milligrams (mg), in an 8-oz serving of selected beverages. Let the beverages listed represent the universal
The symbol < means is approximately ________ to.Fill in the blank with an appropriate word, phrase, or symbol(s).
Use inductive reasoning to predict the next three numbers or figures in the pattern.4, -8, 16, -32, . . .
Your answers may vary from the answers given in the back of the text, depending on how you round your answers. Estimate the answer. There is no one correct estimate. Your answer, however, should be
Your answers may vary from the answers given in the back of the text, depending on how you round your answers. Estimate the answer. There is no one correct estimate. Your answer, however, should be
Use inductive reasoning to predict the next three numbers or figures in the pattern.25, 24, 22, 19, 15, . . .
Quan purchased four tickets to see Luke Bryan at the Ryman Auditorium in Nashville. The tickets cost $113 each plus tax. The sales tax rate in Nashville is 9.25%. Determine the total price Quan paid
Estimate the answers.188,000/0.11
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