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$\left( a \right)$ a + b

$\left( b \right)$ a + b + 1

$\left( c \right)$ ab

$\left( d \right)$ ab + 2

$\left( e \right)$ None of these

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Given data:

a and b are the odd numbers.

Odd numbers

Odd numbers are those which cannot be divisible by 2.

For example: 1, 3, 5 …

Even numbers

Even numbers are those which are divisible by 2.

For example: 2, 4, 6 …

Now consider two different or same odd numbers which represent the given odd number a and b.

Let, a = 3 and b = 5.

Now check options one by one.

Option (a)

a + b = 3 + 5 = 8.

As we know that 8 is divisible by 2 so 8 is an even number.

So a + b is even.

Option (b)

a + b + 1 = 3 + 5 + 1 = 9.

As we know that 9 is not divisible by 2, so 9 is an odd number.

So, a + b + 1 is odd.

Option (c)

ab = 3(5) = 15.

As we know that 15 is not divisible by 2, so 15 is an odd number.

So, ab is odd.

Option (d)

ab + 2 = 3(5) + 2 = 15 + 2 = 17

As we know that 17 is not divisible by 2, so 17 is an odd number.

So, a b + 2 is odd.