Question

Let A = {a, b, {c, d}, e}. Which of the following are false and why ?

(i) {c, d} $\subset$ A (ii) {c, d} $ϵ$ A (iii){{c, d}$ϵ$ A }

(iv) a $ϵ$ A (v) a $\subset$ A (vi) {a, b, e} $\subset$ A

(vii) {a, b, e} $ϵ$ A (viii) {a, b, c} $ϵ$ A (ix) $\varphi$$ϵ$ A (x) { $\varphi$ } $\subset$ A

Answer 1

(i) False, {c, d} is an element of A and not a subset of A.

(ii) True, $\because$ {c, d} is indeed an element of A.

(iii) True, $\because$ {c, d} is a subset of A.

(iv) True,

(v) False, $\because$ a belong to A and not a subset of A. An element of a set belongs to it whereas a subset of it is contained in it.

(vi) True, $\because$ {a, b, e} is a subset of A.

(vii) False, $\because$ {a, b, e} is a subset of A, so it does not belong to A.

(viii) False, $\because$ {a, b, c} is not a subset of A.

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

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