S is a given set and a,b ∈ S. Prove that the operation ∗ defined by a ∗ b = 3a +5b on set S= set of positive integers, is a binary operation.
Here, S is a set of positive integers.
a b = 3a + 5b
The multiplication and addition of integers is always a positive integer.
Thus, for all a, b S, a b = 3a + 5b S
So, it is a binary operation.