Question

Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8 }}. Determine whch of the following is true or false :

(i) 1 $ϵ$ A (ii) {1, 2, 3} $\subset$ A (iii) {6, 7, 8} $ϵ$ A (iv) {{4, 5}} $\subset$ A (v) $\varphi$ $ϵ$ A

Answer 1

(i) False, $\because$ 1 is not an element of A.

(ii) False, $\because$ {1, 2, 3} is not a subset of A, it is an element of A.

(iii) True, $\because$ {6, 7, 8} is indeed an element of A.

(iv) True, $\because$ {{4, 5} } is indeed a subset of A.

(v) False , $\because$ $\varphi$ is a subset and not an element of A.

(vi) True, $\because$ $\varphi$ is a subset of every set, and hence a subset of A.