Chapter 6.2, Problem 1CE

a.

To determine

To state: contrapositive of each statement

Answer to Problem 1CE

If you can’t dance, then I can’t sing.

Explanation of Solution

Given information: The statement is ‘If I can sing, then you can dance’

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’

Given statement is ‘If I can sing, then you can dance’

Contrapositive is If you can’t dance, then I can’t sing.

b.

To determine

To state: contrapositive of each statement

Answer to Problem 1CE

If I can ride a horse, then you can play baseball

Explanation of Solution

Given information: The statement is ‘If you can’t play baseball, then I can’t ride a horse.’

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’

Given statement is ‘If you can’t play baseball, then I can’t ride a horse.’

Contrapositive is If I can ride a horse, then you can play baseball

c.

To determine

To state: contrapositive of each statement

Answer to Problem 1CE

If $x^2-5\ne 11$ , then $x\ne 4$

Explanation of Solution

Given information: The statement is ‘If $x=4$ , then $x^2-5=11$ .’

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’

Given statement is ‘If $x=4$ , then $x^2-5=11$ .’

Contrapositive is If $x^2-5\ne 11$ , then $x\ne 4$

d.

To determine

To state: contrapositive of each statement

Answer to Problem 1CE

If $y=4$ , then $y\ge 3$

Explanation of Solution

Given information: The statement is ‘If $y<3$ , then $y\ne 4$ ’

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’

Given statement is ‘If $y<3$ , then $y\ne 4$ ’

Contrapositive is If $y=4$ , then $y\ge 3$

e.

To determine

To state: contrapositive of each statement

Answer to Problem 1CE

If the sum of the measures of a polygon is not equal to $180°$ , then it is not a triangle.

Explanation of Solution

Given information: The statement is ‘If the polygon is a triangle, then the sum of the measures of its angles is $180°$ ’

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’

Given statement is ‘If the polygon is a triangle, then the sum of the measures of its angles is $180°$ ’

Contrapositive is If the sum of the measures of a polygon is not equal to $180°$ , then it is not a triangle.