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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}}, 

(viii) { ϕ, {ϕ} , {1, ϕ}} A

(ix) {{ ϕ}} A. 


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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