Logic and Reasoning Conditional Statements. Logic The use and study of valid reasoning. When studying mathematics it is important to have the ability.

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Presentation transcript:

Logic and Reasoning Conditional Statements

Logic The use and study of valid reasoning. When studying mathematics it is important to have the ability to think critically and evaluate the validity of statements and conclusions.

Mathematical Sentence A sentence that generally states a fact. Facts are either true or false. Open Sentences – have variables so validity can not be determined. x + 5 = 7 It is the capital of Utah. Closed Sentences – are either true or false = 7 Fillmore is the capital of Utah.

A mathematical sentence written in if- then form is called a conditional statement. Example: An isosceles triangle has two congruent sides. If a triangle is isosceles, then it has two congruent sides.

There are two parts to a conditional statement: The hypothesis follows the “if” and the conclusion follows the “then.” If {hypothesis}, then {conclusion}. If a triangles is isosceles, then it has two congruent sides. Hypothesis – a triangle is isosceles Conclusion – a triangle has two congruent sides

The converse of a conditional statement is formed by exchanging the hypothesis and the conclusion. If {conclusion}, then {hypothesis}. Conditional statement – If it is July, then I don’t have to go to school. Converse – If I don’t have to go to school, then it is July.

The inverse of a conditional statement negate both the hypothesis and the conclusion. If {not hypothesis}, then {not conclusion}. Conditional statement – If it is July, then I don’t have to go to school. Inverse – If it isn’t July, then I have to go to school.

The contrapositive of a conditional statement is the converse of the inverse. If {not conclusion}, then {not hypothesis}. Conditional statement – If it is July, then I don’t have to go to school. Contrapositive – If I have to go to school, then it isn’t July.