Section 2.1 Conditional Statements Standards #1&3 Wednesday, July 06, 2016Wednesday, July 06, 2016Wednesday, July 06, 2016Wednesday, July 06, 2016.

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Presentation transcript:

Section 2.1 Conditional Statements Standards #1&3 Wednesday, July 06, 2016Wednesday, July 06, 2016Wednesday, July 06, 2016Wednesday, July 06, 2016

Goals Recognize Conditional StatementsRecognize Conditional Statements Use the Point, Line and Plane PostulatesUse the Point, Line and Plane Postulates

A type of logical statement that consists of two parts: hypothesis and conclusion. Example: (Can use the “If-then” form) If class is fun, then it must be math!! Conditional Statements: hypothesis conclusion

Converse hypothesis A statement formed by switching the hypothesis and conclusion of a conditional statement. Example: If class is fun, then it is math!! Converse (switch): If it is math, then class is fun!! hypothesis conclusion

Negation The negative or opposite of a statement, can be written 2 ways. Example #1: Statement:I like ice cream. Negation:I don’t like ice cream. Example #2: Statement:I don’t like ice cream. Negation:I do like ice cream.

Inverse A logical statement where the hypothesis and conclusion are both negated. Example: If class is fun, then it is math. Inverse (negate): If class is not fun, then it is not math.

Contrapositive A statement formed by both negating and switching the hypothesis and conclusion of a conditional statement. Example : If class is fun, then it is math. Contrapositive (switch and negate): If it is not math, then class is not fun.

Equivalent Statements Two statements that are either both true or both false. Conditional = Contrapositive Inverse = Converse

Rewrite in If-Then form: Example #1 All elephants have tails. If an animal is an elephant, then it has a tail.

Example #2 Write a counterexample If a number is odd, then it is divisible by three.

Answer to #2 If a number is odd, then it is divisible by three. 7 ÷ 7 = 1. 7 is odd and is not divisible by 3

Example #3 Write the a) converse, b) inverse, and c) contrapositive of the statement: If an animal is a fish, then it can swim.

Answer to #3 If an animal is a fish, then it can swim. If an animal can swim, then it is a fish. If an animal is not a fish, then it cannot swim. If an animal cannot swim, then it it not a fish. Converse (switch): Inverse (negate): Contrapositive (switch & negate):

Assignment Pages a HW # odd