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

Since, Φ belongs to set A. Thus, true.

(ii) True

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

(iii) False

Since, 1 is not an element of A. Thus, false.

(iv) True

Since, {2, Φ} is a subset of A. Thus, true.

(v) False

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

(vi) True

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

(vii) True

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

(viii) True

Here, all three {ϕ, {ϕ}, {1, ϕ}} are subset of set A. Thus, true.

(ix) True

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



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