Question

Let A ⊆ \(\Z\) with 0 ∈ A. For r, s ∈ \(\Z\), define
rA = {ra : a ∈ A},   rA + sA = {ra + sb : a, b ∈ A}.
Which of the following conditions imply that A is a subgroup of the additive group \(\Z\) ?

• A. −2A ⊆ A, A + A = A
• B. A = −A, A + 2A = A
• C. A = −A, A + A = A
• D. 2A ⊆ A, A + A = A

Answer 1

The Correct Option is A, B, C

The correct option is (A) : −2A ⊆ A, A + A = A, (B) : A = −A, A + 2A = A and (C) : A = −A, A + A = A