Chapter 7: Deductive Reasoning - Propositional Logic

Question 1

Propositional Logic

Answer 1

A branch of deductive reasoning that deals with the logical relationships among entire statements

Uses variables as well as logical connectives to symbolize the form of arguments

Question 2

Conjunction

Answer 2

(and), p & q

Priya rode her bike, and John walked

A conjunction is false if at least one of its statement components (conjuncts) is false

Question 3

Disjunction

Answer 3

(or), p v q

Either Priya rode her bike or John walked

A disjunction is still true even if one of its component statements (disjuncts) is false

Question 4

Negation

Answer 4

(not), tilde p

Priya did not ride her bike

A negation is the denial of a statement

Question 5

Conditional

Answer 5

(if - then) p arrow q

If Priya rode her bike, then John walked

A conditional statement is false if and only if its antecedent is true and its consequent is false

Question 6

Checking for Validity

Answer 6

The truth table test of validity is based on a basic, but very important, fact about validity that you’ve already encountered: It’s impossible for a valid argument to have true premises and a false conclusion.

Question 6

Antecedent (p)

Answer 6

The word or phrase that a pronoun refers to or replaces in a sentence

Question 7

Consequent (q)

Answer 7

The second statement (the then part) is known as the consequent

Question 8

Words used in conditionals

Answer 8

“if” —introduces the antecedent; If p, then q = p → q

“only if” —introduces the consequent; p only if q = p → q

“provided” —introduces the antecedent; p provided q = q → p

“unless” —introduces the antecedent; p unless q = ~q → p

“whenever” —introduces the antecedent; whenever p, q = p → q