Page 180 - Math Course 2 (Book 2)

Conditional Statements

inverse
MO. 12 - L3b
negating both the hypothesis and conclusion of
the conditional.
Related Conditionals

If a number is even, then it is
Conditional:
divisible by 2.
If a number is divisible by 2, then
Converse:
Vocabulary A-Z it is even.
Let us learn some vocabulary Inverse: If a number is not even, then it is
not divisible by 2.

If a number is not divisible by 2,
related conditionals Contrapositive: then it is not even.
Other statements based on a given conditional
statement are known as related conditionals. contrapositive
They are in the form of converse, inverse and negating both the hypothesis and conclusion of
contrapositive.
the converse statement.

If a number is even, then it is
Conditional: If a number is even, then it is
divisible by 2. Conditional: divisible by 2.
If a number is divisible by 2, then
Converse: If a number is divisible by 2, then
it is even. Converse: it is even.
If a number is not even, then it is
Inverse: If a number is not even, then it is
not divisible by 2. Inverse: not divisible by 2.
If a number is not divisible by 2,
Contrapositive: If a number is not divisible by 2,
then it is not even. Contrapositive:
then it is not even.
converse
exchanging the hypothesis and conclusion of the logically equivalent
conditional. Statements with the same truth values are said to
be logically equivalent.
If a number is even, then it is
Conditional:
divisible by 2. A conditional and its contrapositive are logically
equivalent. The converse and inverse of a condi-
If a number is divisible by 2, then
Converse: tional are logically equivalent. These relationship
it is even. are summarized in the table.
If a number is not even, then it is
Inverse: Conditional Converse Inverse Contrapositive
not divisible by 2. p q p –> q q –> p ~p –> ~q ~p –> ~q
If a number is not divisible by 2, T T T T T T
Contrapositive:
then it is not even. T F F T T F

Key Concept F T T F F T
T
T
T
T
F
F
Related Conditionals

Statement Formed by Symbols Examples

If two angles have the same measure,
Conditional given hypothesis and conclusion p → q
then they are congruent.

Converse exchanging the hypothesis and q → p If two angles are congruent, then they
conclusion of the conditional
have the same measure.
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