If , then
is any odd multiple of and is any multiple of
Explanation for the correct option
Step 1: Simplification of the given relation
We can write the given relation as
Use the formula of ,
Let then we have,
From this, we can see that either or
Step 2: Check for
We know that when then is equal to .
Let be any integer such that when it is multiplied by then it gives the value zero when is applied.
If we put the values of like then we can deduce that,
will not be equal to when is even so it must be odd. And odd integers are written in the form .
From this, we have that is any odd multiple of .
Step 3: Check for
We know that when then is either or
If we multiply any integer with , the value of will be zero.
From this, we have that is any multiple of .
Hence, the correct option is (A).