Conditional statement p→q Converse statement q→p

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Presentation transcript:

Conditional statement p→q Converse statement q→p UNIT 2 Biconditionals and Definitions 2.4 The converse of a conditional statement is when the hypothesis and conclusion are exchanged. Conditional statement p→q Converse statement q→p If you study more then your grades improve The converse is :

UNIT 2 Biconditionals and Definitions 2.4 Write the converse for each conditional statement. If you go to the zoo, then you will see animals. If you drive slower, then your gas mileage will improve. If it is a triangle, then it is a 3-sided polygon.

UNIT 2 Biconditionals and Definitions 2.4 A biconditional statement is a statement that can be written in the form “p if and only if q.” This means both “p → q” and “q → p.” The biconditional “p if and only if q” can also be written as “p iff q” or p  q. Write the statements as biconditionals. If you go to the zoo, then you will see animals.

UNIT 2 Biconditionals and Definitions 2.4 If you drive slower, then your gas mileage will improve. You drive slower if and only if your gas mileage will improves. If it is a triangle, then it is a 3-sided polygon. It is a triangle iff it is a 3-sided polygon.

UNIT 2 Biconditionals and Definitions 2.4 Given each biconditional statement, write the conditional and the converse An angle is obtuse iff its measure is greater than 90 and less than 180 CS: if an angle is obtuse, then its measure is > 90° and < 180° Con: If the measureis > 90° and < 180°, then the angle is obtuse 2x + 3 = 11 iff x = 4

UNIT 2 Biconditionals and Definitions 2.4 The conditional and converse each have a truth value. The truth value of the conditional and converse may or may not be the same. Determine the truth value of each previous conditional and converse If you drive slower, then your gas mileage will improve. If your gas mileage will improves, then you drive slower. If it is a triangle, then it is a 3-sided polygon. If it is a 3-sided polygon, then it is is a triangle.

UNIT 2 Biconditionals and Definitions 2.4 If both the conditional and converse are both TRUE, Then the biconditional is also TRUE Hint…to determine if a biconditional is true, see if you can find a counterexample to the conditional or converse statement. Determine if the biconditonals are TRUE or FALSE. A figure is a triangle iff it is a 3-sided polygon. A figure is square iff it has 4 right angles.

UNIT 2 Biconditionals and Definitions 2.4 In geometry, biconditional statements are used to write definitions. Write each definition as a biconditional. A pentagon is a five-sided polygon. A figure is a pentagon if and only if it is a 5-sided polygon. A right angle measures 90°. An angle is a right angle if and only if it measures 90°.

An apple is a fruit that contains seeds. UNIT 2 Biconditionals and Definitions 2.4 To determine if a definition is good, evaluate the biconditional. An apple is a fruit that contains seeds.

Homework: 2.4(99):10,14,16,19,21,22,32