Chapter 1 Flashcards by jerry Kim

Truth Table for Negation of Proposition:

when P is TRUE,
¬P is ___

FALSE

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Truth Table for Negation of Proposition:

when P is FALSE,
¬P is ___

TRUE

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The Truth Table for the Conjunction of Two Propositions:

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

TRUE

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The Truth Table for the Conjunction of Two Propositions:

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

FALSE

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The Truth Table for the Conjunction of Two Propositions:

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

FALSE

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The Truth Table for the Conjunction of Two Propositions:

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

FALSE

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The Truth Table for the DISJUNCTION of Two Propositions:

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

TRUE

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The Truth Table for the DISJUNCTION of Two Propositions:

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

TRUE

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The Truth Table for the DISJUNCTION of Two Propositions:

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

TRUE

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The Truth Table for the DISJUNCTION of Two Propositions:

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

FALSE

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What is:

P ⊕ Q

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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The Truth Table for the Exclusive Or of Two Propositions:

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

FALSE

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The Truth Table for the Exclusive Or of Two Propositions:

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

TRUE

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The Truth Table for the Exclusive Or of Two Propositions:

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

TRUE

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The Truth Table for the Exclusive Or of Two Propositions:

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

FALSE

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In P → Q, what is the HYPOTHESIS?

also called the ANTECEDENT or PREMISE

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In P → Q, what is the CONCLUSION?

also called the CONSEQUENCE

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

“If P, then Q”

P only if Q;

Q unless ¬P;

The Truth Table for the Conditional Statement P → Q.

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

TRUE

The Truth Table for the Conditional Statement P → Q.

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

FALSE

The Truth Table for the Conditional Statement P → Q.

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

TRUE

The Truth Table for the Conditional Statement P → Q.

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

TRUE

What is the CONVERSE of P → Q?

Q → P

What is the CONTRAPOSITIVE of P → Q?

¬Q → ¬P

What is the INVERSE of P → Q?

¬P → ¬Q

Which of the following has the same truth statements as P → Q: CONVERSE, CONTRAPOSITIVE, or INVERSE?

CONTRAPOSITIVE

What does it mean for two propositions to be EQUIVALENT?

They have the same truth values

What are the contrapositive, the converse, and the inverse of the conditional statement “The home team wins whenever it is raining?”

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.”

What is: P ↔ Q

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.

Truth Table for BICONDITIONAL P ↔ Q: if P is TRUE, & Q IS TRUE, P ↔ Q is ___

TRUE

Truth Table for BICONDITIONAL P ↔ Q: if P is TRUE, & Q IS FALSE, P ↔ Q is ___

FALSE

Truth Table for BICONDITIONAL P ↔ Q: if P is FALSE, & Q IS TRUE, P ↔ Q is ___

FALSE

Truth Table for BICONDITIONAL P ↔ Q: if P is FALSE, & Q IS FALSE, P ↔ Q is ___

TRUE

What is a tautology?

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

What does it mean to be logically equivalent?

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

What is a contradiction?

A compound proposition that is always false

What is a contingency?

A compound proposition that is neither a tautology nor a contradiction

what is ∀xP(x)?

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

what is a COUNTEREXAMPLE

an element for which P(x) is false

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?

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.

what is ∃xP(x)

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