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| PAGE: 626 | SET: Exercises | PROBLEM: 37 |
Statement : 
is divisible by 
.
The statement is False.
Proof :
Let 
be the statement 
is divisible by 
.
is the statement that 
is divisible by ,
is true since 
which is divisible by .
Assume 
is true where 
is a positive integer and we have to prove that 
must be
true i.e., show that 
for some integer 
implies that 
is divisible by .
Plug in differerent values :
For 
:
which is not divisible by but divisible by 
.
For 
:
which is divisible by .
For 
:
which is not divisible by but divisible by 
.
Therefore, is divisible by only when 
is an odd number.
The expression is not divisible by .
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