Discrete Mathematics  (Mathematics 1271)

Let S be the set of irrational numbers and ∆ be the addition. Is S closed under ∆? Justify your answer

Let S be the set of positive integers Z+ and ∆ be the subtraction. Is S closed under ∆? Justify your answer

Let S be the set of nonzero rational numbers Q \ {0} and ∆ be the division. Is S closed under ∆?

Consider the following sets S, with respective operator ∆. 1. Let S be the set of odd integers and ∆ be the multiplication. Is S closed under ∆? Justify your answer.