1.

Let A = {ϕ, {ϕ}, 1, {1, ϕ}, 2}. Which of the following are true? (i) ϕ ∈ A (ii) {ϕ} ∈ A (iii) {1} ∈ 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.

Answer»

(i) True 

Φ is a member of set A. Hence, true. 

(ii) True 

{ Φ} is a member of set A. Hence, true. 

(iii) False 

1 alone is not a member of A. Hence, false. 

(iv) False 

We can see that 2 is a member of set A, {2, Φ} is not. Hence, false 

(v) True 

2 is a member of set A. Hence, true. 

(vi) True 

{1} is not a member of set A. 

(vii) True 

Neither {2} and nor {1} is a member of set A. Hence, true. 

(viii) True 

All three are members of set A. Hence, true. 

(ix) False 

{{ϕ}} is not a member of set A. Hence, false



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