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Chapter 6: Q22. (page 212)

Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.

If n2is not a multiple of 3, then n is not a multiple of 3.

Short Answer

Expert verified

Hence proved that if n2is not a multiple of 3, then n is not a multiple of 3.

Step by step solution

01

Step 1. Define contrapositive statement

If the given statement is 鈥樷�橧f p then q鈥欌��, the contrapositive is 鈥樷�橧f not q then not p鈥欌赌�.

The given statement is if n2 is not a multiple of 3, then n is not a multiple of 3.

02

Step 2. Let the given statement and find its contrapositive

The contrapositive of the given statement is if n is not a multiple of 3 then n2is not a multiple of 3.

03

Step 3. Prove the statement

Suppose the values for n are 3,6,9.

Then the value of n2will be:

role="math" localid="1638187118341" n2=32=9n2=62=36

Also, . Hence n2=92=81is also the multiple of 3.

Hence proved.

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