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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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