If an odd number is multiplied by an odd number, then the product is odd.

Let the odd number *A* multiplied by the odd number *B* make *C.*

I say that *C* is odd.

Since *A* multiplied by *B* makes *C,* therefore *C* is made up of as many numbers equal to *B* as there are units in *A.* And each of the numbers *A* and *B* is odd, therefore *C* is made up of odd numbers, the multitude of which is odd. Thus *C* is odd.

Therefore, *if an odd number is multiplied by an odd number, then the product is odd.*

Q.E.D.