Definitions Chapter 5

Question 0

Statement

Answer 0

A sentence that is either true or false, but not both

Question 1

Reasoning

Answer 1

Is the step-by-step process that begins with a known fact or assumption and builds to a conclusion in an orderly, concise way. This is also called logical thinking

Question 2

Conjunction

Answer 2

A statement in which two statement in which two statements, p and q is denoted p^q

Question 3

Disjunction

Answer 3

Is a statement in which two statements, p and q are connected by or. The notation for the disjunction p or w is denoted pVq

Question 4

Conditional statement

Answer 4

A statement of the form “if p, then q,” where p and q are statements. The notation for this conditional statement is p—>q

Question 5

Biconditional statement

Answer 5

A statement of the form “p if and only if q” ( symbolized by pq), which means p—> q and q—> p.

Question 6

Converse

Answer 6

The converse of a conditional statement is obtained by switching the hypothesis and conclusion. The converse of p—>q is q—>q

Question 7

Inverse

Answer 7

The inverse of a conditional statement is obtained by negating both hypothesis and conclusion. The inverse of p—>q is ~p—>~q

Question 8

Contrapositive

Answer 8

The contrapositive of a conditional statement is obtained by switching and negating the hypothesis and conclusion. The contrapositive of
p—>q is ~q—>~p

Question 9

Proof

Answer 9

A system of reasoning or argument to convince a person of the truth of a statement

Question 10

Inductive reasoning

Answer 10

An argument to establish that a statement is probably true

Question 11

Deductive reasoning

Answer 11

An argument to establish that a statement is absolutely certain

Question 12

An argument is valid if…..

Answer 12

The reasoning proceeds logically from the premises to the conclusion

Question 13

An argument is sound if…..

Answer 13

It is valid and the premises are true

Question 14

Modus ponens

Answer 14

P->q
P
Q

Question 15

Modus tollens

Answer 15

P->q
~q
~p