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Chapter 1: Q51. (page 59)

Which value of bserves as a counterexample to the statement 2b<3b?

A. 鈭�4 C. 12

B. 14 D. 4

Short Answer

Expert verified

The correct choice is Option A b=鈭�4.

Step by step solution

01

Step 1. State the concept.

A counterexample to a statement is a case which makes the statement false.

02

Step 2. List the given data.

The given statement is 鈥�2b<3b鈥�.

03

Step 3. Solve.

Solving the given statement,

2b<3b2b鈭�2b<3b鈭�2b0<bb>0

So, the given statement is true for all b>0.

04

Step 4. Determine the counterexample.

Since a counterexample makes the statement false, it must be a value such that b<0.

Of the given options, the only value of b, for which b<0is option A b=鈭�4

So, the correct choice is Option A b=鈭�4.

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