

InterviewSolution
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if A = {3, {4, 5}, 6} find which of the following statements are true.(i) {4, 5} ⊄A (ii) {4, 5} ϵA (iii) {{4, 5}} ⊆A (iv) 4ϵA (v) {3} ⊆A (vi) {ϕ} ⊆A (vii) ϕ⊆A (viii) {3, 4, 5} ⊆A (ix) {3, 6} ⊆A |
Answer» (i) True Explanation: we have, A = {3, {4, 5}, 6} Let {4,5} = x Now, A = {3, x, 6} 4,5 is not in A, {4,5} is an element of A and element cannot be subset of set,thus {4, 5} ⊄A. (ii) True Explanation: we have, A = {3, {4, 5}, 6} Let {4,5} = x Now, A = {3, x, 6} Now, x is in A. So, x ∈ A. Thus, {4, 5} ϵ A (iii) True Explanation: {4,5} is an element of set {{4,5}}. Let {4,5} = x {{4,5}} = {x} we have, A = {3, {4, 5}, 6} Now, A = {3, x, 6} So, x is in {x} and x is also in A. So , {x} is a subset of A. Hence, {{4, 5}} ⊆A (iv) False Explanation: 4 is not an element of A. (v) True Explanation: 3 is in {3} and also 3 is in A. (vi) False Explanation: ϕ is an element in { ϕ} but not in A. Thus, {ϕ} ⊄ A (vii) True Explanation: ϕ is a subset of every set. (viii) False Explanation: we have, A = {3, {4, 5}, 6} Let {4,5} = x Now, A = {3, x, 6} 4,5 is in {3,4,5} but not in A, thus {3,4, 5} ⊄A. (ix) True Explanation: 3,6 is in {3,6} and also in A, thus {3, 6} ⊆A. |
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