Page 335 - Algebra 1

INVE5STIGATION
Using Logical Reasoning
Recall from Investigation 4 that a conditional statement has a hypothesis and a conclusion. For any conditional statement, a converse, inverse, and contrapositive can be written.
In the converse of a conditional statement the order of the hypothesis and conclusion of the original statement is reversed.
The inverse of a conditional statement negates both the hypothesis and the conclusion.
Original
Converse
If a figure is a triangle, then it has three sides.
If a figures has three sides, then it is a triangle.
Original
Inverse
If a figure is a triangle, then it has three sides.
If a figure is not a triangle, then it does not have three sides.
Math Language
To negate a statement means to state its opposite using the word not.
The contrapositive switches the hypothesis and the conclusion and negates both.
Write the given statement in the form indicated. Note whether the new statement is true or false. If false, give a counterexample.
1. Write the converse. If a number ends in 5, then it is a multiple of 5.
2. Write the contrapositive. If two lines are parallel, then they do not
meet.
3. Write the inverse. If it is Monday, then I will go to school.
4. Write the inverse. If a number is even, then it is divisible by two.
The statement, “Dallas is the capital of New York,” is false. However, saying “Dallas is not the capital of New York” is true. The truth value of a statement is either true or false.
5. Complete the tables to compare the truth values of an original statement and its contrapositive.
Original
Contrapositive
If a figure is a triangle, then it has three sides.
If a figure does not have three sides, then it is not a triangle.
Original
True or False
Contrapositive
True or False
If a figure is a square, then it is a rectangle.
If a number is odd, then it is divisible by 2.
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