Chapter 6.2, Problem 2CE

a.

To determine

To state: inverse of each statement

Answer to Problem 2CE

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

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 inverse is ‘’If not p then not q’’

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

Inverse is ‘If I can’t sing, then you can’t dance’

b.

To determine

To state: inverse of each statement

Answer to Problem 2CE

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

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 inverse is ‘’If not p then not q’’

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

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

c.

To determine

To state: inverse of each statement

Answer to Problem 2CE

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

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 inverse is ‘’If not p then not q’’

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

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

d.

To determine

To state: inverse of each statement

Answer to Problem 2CE

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

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 inverse is ‘’If not p then not q’’

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

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

e.

To determine

To state: inverse of each statement

Answer to Problem 2CE

If the polygon is not a triangle, then the sum of the measures of its angles is not $180°$

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 inverse is ‘’If not p then not q’’

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

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