1B - Propositions and Truth Values

Question 1

What is a proposition?

Answer 1

A statement that makes a claim that is either true or false. It is the building block of an argument.

Question 2

A proposition must have the structure of a ____(1)____ and make a distinct ____(2)____ or ____(3)____.

Answer 2

(1) sentence; (2) assertion; (3) denial

Question 3

What is a negation?

Answer 3

A proposition’s opposite. IF P is a proposition, then NOT P is its negation.

Question 4

What is a truth value?

Answer 4

The verifiable, “yes or no” answer of a proposition.

Question 5

What is a truth table?

Answer 5

A table with a row for each possible set of truth values for the propositions being considered.

Question 6

Double negations have the same truth value as…

Answer 6

their original propositions.

Question 7

Examples of logical connectors

Answer 7

and; or; if…then

Question 8

Conjunctions

Answer 8

A compound statement made with the logical connector AND. A conjunction is true ONLY if both propositions are true.

Question 9

Disjunctions

Answer 9

A compound statement made with the logical connector OR, which is used inclusively to indicate “either or both”. Hence, a disjunction is FALSE only when both propositions are false. Otherwise it’s true.

Question 10

Conditionals/Implications

Answer 10

A compound statement using the words “if…then… to join two propositions. For example, “if p, then q”. A conditional is only FALSE when what is implied (p) doesn’t lead to the promised conclusion (q).

Question 11

Hypothesis/Antecedent

Answer 11

The “if”/p proposition in a conditional.

Question 12

Conclusion/Consequent

Answer 12

The “then/q proposition in a conditional.

Question 13

Alternate phrasings of conditionals

Answer 13

p is sufficient for q
p will lead to q
p implies q
q is necessary for p
q is p
q whenever p

Question 14

Converse

Answer 14

The result of switching the order of the propositions of a conditional statement. Example - “if q, then p”

Question 15

Inverse

Answer 15

The result of negating the propositions in a conditional statement. Ex. “if not p, then not q”

Question 16

Contrapositive

Answer 16

The result of both switching the order of and negating the propositions in a conditional statement. Example: “if not q, then not p”

Question 17

Two statements are logically equivalent if they share the same ___________.

Answer 17

truth values