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Chapter 1: Q36. (page 57)

Example 4 Find a counterexample for each conditional statement.

If 3x+17鈮�53then x<12.

Short Answer

Expert verified

The statement that if 3x+17鈮�53,, then x<12 is not true and the counterexample is x=12.

Step by step solution

01

Step 1. Given Statement.

3x+17鈮�53,

02

Step 2. Description of step.

To find a counterexample for the given statement, solve the given expression and find the value of xas

03

Step 3. Calculation.

3x+17鈮�53鈬�3x鈮�53鈭�17鈬�3x鈮�36鈬�x鈮�363鈬�x鈮�12

But it is given in the statement that x<12.

But from the solution above it also satisfy for x=12, as

3x+17=312+17=36+17=53

Since the statement is true for x=12also.

Hence the statement that if 3x+17鈮�53,then x<12is not true, and counterexample is x=12.

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