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Chapter 2: Q14 (page 34)

State the converse of each conditional. Is the converse true or false?

If a number is divisible by 6, then it is divisible by 3.

Short Answer

Expert verified

The converse of the given statement is " If a number is divisible by 3, then it is divisible by 6鈥� and the converse is false.

Step by step solution

01

Step 1. Converse of a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement 鈥淚f p, then q鈥� will be 鈥淚f q, then p鈥�.

02

Step 2. Write the converse of the statement.

Consider the statement 鈥淎 number is divisible by 6 then, it is divisible by 3鈥�.

Clearly, a number that is divisible by 6 is also divisible by 3.

Therefore, the statement is true.

Consider p is "a number is divisible by 6鈥� and q is "it is divisible by 3鈥�.

The converse is of the form "if q, then p鈥�

Therefore, the converse of the given statement is: 鈥淚f a number is divisible by 3, then it is divisible by 6鈥�.

03

Step 3. Verify the converse of the statement.

Consider the number 9, it is divisible by 3 but not by 6.

Therefore, the converse of the given statement is false.

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