-  Product of two odd numbers is always odd.

To understand why this is the case, we need to first define what is meant by an odd number. An odd number is an integer that is not divisible by 2, or equivalently, an integer that leaves a remainder of 1 when divided by 2.

Let's take a look at the other options:

A. Sum of two odd numbers: This is not always odd. For example, 3 + 5 = 8, which is even.

C. Difference of two odd numbers: This is not always odd. For example, 7 - 3 = 4, which is even.

D. Sum of two even numbers: This is not always odd. In fact, the sum of two even numbers is always even.

E. None of these: This is not correct. We have already shown that option B is always odd.

So, we are left with option B, the product of two odd numbers. Let's take two odd numbers, x and y, and multiply them together:

x = 2a + 1 (since x is odd)

y = 2b + 1 (since y is odd)

xy = (2a + 1)(2b + 1)

= 4ab + 2a + 2b + 1

= 2(2ab + a + b) + 1

We can see that the product xy can be expressed in the form 2c + 1, where c = 2ab + a + b. Since c is an integer, this means that xy is odd.

Therefore, the correct answer is option B, the product of two odd numbers, which is always odd.