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

Asked by Aaryan | 1 year ago |  61

##### Solution :-

(i) True

Φ belongs to set A. Hence, true.

(ii) True

{Φ} is an element of set A. Hence, true.

(iii) False

1 is not an element of A. Hence, false.

(iv) True

{2, Φ} is a subset of A. Hence, true.

(v) False

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

(vi) True

{2, {1}} is not a subset of set A. Hence, true.

(vii) True

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

(viii) True

All three {ϕ, {ϕ}, {1, ϕ}} are subset of set A. Hence, true.

(ix) True

{{ϕ}} is a subset of set A. Hence, true.

Answered by Sakshi | 1 year ago

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