Logic Unit Math

Statement

A statement is a sentence that is either true or false

Represented using letters such a p or q

Negation

A negation of a statement has the opposite truth value.

Shown by the symbol ~p (read as not p)

Compound

Two or more statements joined by the words “and” or “or”.

Conjunction

Statements joined by the word “and”.

Written as p∧q.

True when both statements are true.

Disjunction

Statements joined by the word “or”.

Written as p V q.

True when at least one statement is true.

Conditional Statements

A statement that can be written in “if-then form”

Symbolic form:p → q. (Read as “if p, then q” or, “p implies q”.)

The hypothesis is the phrase that immediately follows if.

The conclusion is the phrase that immediately follows then.

Inverse

Formed by negating (opposite) the hypothesis and conclusion.

~ p→ ~ q

Converse

Formed by switching the hypothesis and conclusion.

q→p

Contrapositive

Formed by negating and switching the hypothesis and conclusion.

~q→~p