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wDiscrete Mathematics > Chapter 1 > Flashcards

Chapter 1 Flashcards

1
Q

Truth Table for Negation of Proposition:

when P is TRUE,
¬P is ___

A

FALSE

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2
Q

Truth Table for Negation of Proposition:

when P is FALSE,
¬P is ___

A

TRUE

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3
Q

The Truth Table for the Conjunction of Two Propositions:

When P is TRUE & Q is TRUE,
P ∧ Q is ___

A

TRUE

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4
Q

The Truth Table for the Conjunction of Two Propositions:

When P is TRUE & Q is FALSE,
P ∧ Q is ___

A

FALSE

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5
Q

The Truth Table for the Conjunction of Two Propositions:

When P is FALSE & Q is TRUE,
P ∧ Q is ___

A

FALSE

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6
Q

The Truth Table for the Conjunction of Two Propositions:

When P is FALSE & Q is FALSE,
P ∧ Q is ___

A

FALSE

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7
Q

The Truth Table for the DISJUNCTION of Two Propositions:

When P is TRUE & Q is TRUE,
P ∨ Q is ___

A

TRUE

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8
Q

The Truth Table for the DISJUNCTION of Two Propositions:

When P is TRUE & Q is FALSE,
P ∨ Q is ___

A

TRUE

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9
Q

The Truth Table for the DISJUNCTION of Two Propositions:

When P is FALSE & Q is TRUE,
P ∨ Q is ___

A

TRUE

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10
Q

The Truth Table for the DISJUNCTION of Two Propositions:

When P is FALSE & Q is FALSE,
P ∨ Q is ___

A

FALSE

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11
Q

What is:

P ⊕ Q

A

EXCLUSIVE OR;

The “exclusive or” of p and q, denoted by p ⊕ q, is the proposition that is true when exactly one of p and q is true and is false otherwise.

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12
Q

The Truth Table for the Exclusive Or of Two Propositions:

When P is TRUE & Q is TRUE,
P ⊕ Q is ___

A

FALSE

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13
Q

The Truth Table for the Exclusive Or of Two Propositions:

When P is TRUE & Q is FALSE,
P ⊕ Q is ___

A

TRUE

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14
Q

The Truth Table for the Exclusive Or of Two Propositions:

When P is FALSE & Q is TRUE,
P ⊕ Q is ___

A

TRUE

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15
Q

The Truth Table for the Exclusive Or of Two Propositions:

When P is FALSE & Q is FALSE,
P ⊕ Q is ___

A

FALSE

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16
Q

In P → Q, what is the HYPOTHESIS?

A

P

also called the ANTECEDENT or PREMISE

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17
Q

In P → Q, what is the CONCLUSION?

A

Q

also called the CONSEQUENCE

18
Q

What are two other ways to say In P → Q, in English other than

“If P, then Q”

A

P only if Q;

Q unless ¬P;

19
Q

The Truth Table for the Conditional Statement P → Q.

When P is TRUE, & Q is TRUE,
P → Q is ___

A

TRUE

20
Q

The Truth Table for the Conditional Statement P → Q.

When P is TRUE, & Q is FALSE,
P → Q is ___

A

FALSE

21
Q

The Truth Table for the Conditional Statement P → Q.

When P is FALSE, & Q is TRUE,
P → Q is ___

A

TRUE

22
Q

The Truth Table for the Conditional Statement P → Q.

When P is FALSE, & Q is FALSE,
P → Q is ___

A

TRUE

23
Q

What is the CONVERSE of P → Q?

A

Q → P

24
Q

What is the CONTRAPOSITIVE of P → Q?

A

¬Q → ¬P

25
Q

What is the INVERSE of P → Q?

A

¬P → ¬Q

26
Q

Which of the following has the same truth statements as P → Q:

CONVERSE, CONTRAPOSITIVE, or INVERSE?

A

CONTRAPOSITIVE

27
Q

What does it mean for two propositions to be EQUIVALENT?

A

They have the same truth values

28
Q

What are the contrapositive, the converse, and the inverse of the conditional statement

“The home team wins whenever it is raining?”

A

CONTRAPOSITIVE: “If the home team does not win, then it is not raining.”

CONVERSE: “If the home team wins, then it is raining.”

INVERSE: “If it is not raining, then the home team does not win.”

29
Q

What is:

P ↔ Q

A

P if and only if Q (biconditional)

The biconditional statement P ↔ Q is true when p and q have the same truth values, and is false otherwise. Biconditional statements are also called bi-implications.

30
Q

Truth Table for BICONDITIONAL P ↔ Q:

if P is TRUE, & Q IS TRUE,
P ↔ Q is ___

A

TRUE

31
Q

Truth Table for BICONDITIONAL P ↔ Q:

if P is TRUE, & Q IS FALSE,
P ↔ Q is ___

A

FALSE

32
Q

Truth Table for BICONDITIONAL P ↔ Q:

if P is FALSE, & Q IS TRUE,
P ↔ Q is ___

A

FALSE

33
Q

Truth Table for BICONDITIONAL P ↔ Q:

if P is FALSE, & Q IS FALSE,
P ↔ Q is ___

A

TRUE

34
Q

What is a tautology?

A

a compound proposition that is always true no matter what the truth values of the variables in it are.

35
Q

What does it mean to be logically equivalent?

A

When compound propositions that have the same truth values in all possible cases are called logically equivalent

this also means that if p ↔ q is a tautology, then p and q are logically equivalent p ≡ q

36
Q

What is a contradiction?

A

A compound proposition that is always false

37
Q

What is a contingency?

A

A compound proposition that is neither a tautology nor a contradiction

38
Q

what is

∀xP(x)?

A

universal quantification of P(x), read “for all xP(x)” or “for every xP(x).”

39
Q

what is a COUNTEREXAMPLE

A

an element for which P(x) is false

40
Q

Let Q(x) be the statement “x < 2.” What is the truth value of the quantification ∀xQ(x), where the domain consists of all real numbers?

A

Q(x) is not true for every real number x, because, for instance, Q(3) is false. That is, x = 3 is a counterexample for the statement ∀xQ(x).

Thus ∀xQ(x) is false.

41
Q

what is

∃xP(x)

A

existential quantification

“There exists an element x in the domain such that P(x).”

wDiscrete Mathematics (9 decks)

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