Chapter 1, Problem 22RP

To determine

To find: The converse, inverse and contrapositive of the given statement and find whether the statements are true or false.

Answer to Problem 22RP

The converse and inverse of the given statement is false, while the contrapositive is true.

Explanation of Solution

Given Info:The following statement is given in the question:

“If the time is $02:00$ , then angle formed by the hand of the clock is acute”

$\Rightarrow$ The converse of the statement is obtained by reversing constituents of the statement.

  $\therefore$ The converse of the statement “If the time is $2:00$ , then the angle formed by the hands of a clock is acute” will be “If the angle formed by the hands of a clock, then it is $2:00$ .”

This statement is false as acute angle can be formed with other times of the clock also.

  $\Rightarrow$ The inverse of a statement is obtained by making the constituents of the statement negative.

  $\therefore$ The inverse of the statement “If the time is $2:00$ , then the angle formed by the hands of a clock is acute” will be “If the time is not $2:00$ , then the angle formed by the hands of a clock is not acute.”

This statement is also false as acute angle can be formed with other times of the clock also.

  $\Rightarrow$ The contrapositive of statement is obtained by interchanging the constituents of the inverse of that statement.

  $\therefore$ The contrapositive of the statement “If the time is $2:00$ , then the angle formed by the hands of a clock is acute” will be “If the angle formed by the hands of the clock is not acute, then the time is not $2:00$ .”

This statement is true, as the angle formed by $2:00$ on a clock is acute.