Question

A subgroup has the properties of ________

(a) Closure, associative

(b) Commutative, associative, closure

(c) Inverse, identity, associative

(d) Closure, associative, Identity, Inverse

This question was addressed to me in homework.

My doubt stems from Group Axioms in section Groups of Discrete Mathematics

Answer 1

Right answer is (d) Closure, associative, Identity, Inverse

To elaborate: A subgroup S is a subset of a group G (denoted by S <= G) if it holds the four properties simultaneously – Closure, Associative, Identity and Inverse element.