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Question

Let A = {ϕ {ϕ}, 1, {1, ϕ}, 2}. Which of the following are true ?

(i) ϕ ϵ A (ii) {ϕ} ϵ A

(iii) {1} ϵ A (iv) {2, ϕ} A

(v) 2 A (vi) {2, {1}} A

(vii) {{2}, {1}}, A

(viii) { ϕ, {ϕ} , {1, ϕ}} A

(ix) {{ ϕ}} A.

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Solution

(i) True, ϕ indeed belongs to A.

(ii) True, {ϕ} is an element of A.

(iii) False, {1} is not an element of A.

(iv) True,

{2, ϕ} is a subset of A.

(v) False,

2 is not a subset of A, it is an element of A.

(vi) True, {2, {1}} is not a subset of A.

(vii) True, {2, {1}} is not a subset of A.

(viii) True, {ϕ, {ϕ}, {1, ϕ}} is a subset of A.

(ix) True, {{ϕ }} is a subset of A.


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