Conditional Statements

Conditional Statements

Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is logical statement that has two parts: The hypothesis is the “if” part of the conditional statement. The conclusion is the “then” part of the conditional statement.

Writing a conditional statement: The hypothesis tells you what you are talking about, and the conclusion describes the hypothesis.

Writing a conditional statement • Writing the following statements in if-then form. Two angles that make a linear pair are supplementary. All 90o angles are right angles.

Vocabulary • The negation of a statement is the opposite of the original.

Negation • Negate the following statements. The ball is red. The cat is not black.

Definitions: Inverse, Converse, Contrapositive • The inverse of a conditional statement negates the hypothesis and conclusion • The converse of a conditional statement switches the hypothesis and conclusion. • The contrapositive of a conditional statement takes the inverse of the converse.

Writing statements • Write the inverse, converse and contrapositive of the conditional statement: “If two angles form a linear pair, then they are supplementary.” Which statements are always true?

Definition: Biconditional: If a conditional statement and its converse are both true, then we can write it as a biconditional statement by using the phrase if and only if instead of putting it in if-then form.

Biconditional Statement • Write the following conditional statement as a biconditional statement. • If two lines intersect to form a right angle, then they are perpendicular.

Conditional Statements