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Write the inverse of the following statement.

a. If I can sing, then you can dance.

b. If you can鈥檛 play baseball, then I can鈥檛 ride a horse.

c. If x=4thenx2-5=11.

d. If y<3then y4.

e. If the polygon is a triangle, then the sum of the measures of its angles is 180鈥.

Short Answer

Expert verified

a. The inverse of the statement is 鈥業f I can鈥檛 sing, then you can鈥檛 dance鈥.

b. The inverse of the statement is 鈥業f you can play baseball, then I can ride a horse.鈥

c. The inverse is 鈥淚f x4, then x2-511.

d. The inverse is 鈥淚f y3 then y=4鈥.

e. The inverse is 鈥淚f the polygon is not a triangle, then the sum of the measures of its angles is not 180.鈥

Step by step solution

01

a.Step 1- Apply the concept of inverse of the conditional statement.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

02

Step 2- Step description.

Given statement is 鈥業f I can sing, then you can dance鈥.

Inverse is 鈥業f I can鈥檛 sing, then you can鈥檛 dance鈥.

03

Step 3- Step description.

Therefore, the inverse of the statement is 鈥業f I can鈥檛 sing, then you can鈥檛 dance鈥.

04

b.Step 1- Apply the concept of inverse of the conditional statement.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

05

Step 2- Step description.

The statement is 鈥業f you can鈥檛 play baseball, then I can鈥檛 ride a horse.鈥

Inverse is If you can play baseball, then I can ride a horse.鈥

06

Step 3- Step description.

Therefore, the inverse of the statement is 鈥業f you can play baseball, then I can ride a horse.鈥

07

c.Step 1- Apply the concept of inverse of the conditional statement.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

08

Step 2- Step description.

The statement is 鈥業f x=4, then x2-5=11.鈥

Inverse is 鈥淚f x4, then x2-511鈥.

09

Step 3- Step description.

Therefore, the inverse of the statement is 鈥業f x4, then x2-511鈥.

10

d.Step 1- Apply the concept of inverse of the conditional statement.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

11

Step 2- Step description.

The statement is 鈥業f y<3, then y4鈥.

Inverse is 鈥淚f y3, then y=4.鈥

12

Step 3- Step description.

Therefore, the inverse of the statement is 鈥淚fy3, then y=4.鈥

13

e.Step 1- Apply the concept of inverse of the conditional statement.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

14

Step 2- Step description.

The statement is 鈥業f the polygon is a triangle, then the sum of the measures of its angles is 180鈥.

Inverse is If the polygon is not a triangle, then the sum of the measures of its angles is not 180.

15

Step 3- Step description.

Therefore, the inverse of the statement is 鈥渋s If the polygon is not a triangle, then the sum of the measures of its angles is not180.鈥

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