Which of the following statements are correct? Write a correct form of

1.	Which of the following statements are correct? Write a correct form of each of the incorrect statements.(i) a ⊂ {a, b, c}(ii) {a} {a, b, c}(iii) a {{a}, b}(iv) {a} ⊂ {{a}, b}(v) {b, c} ⊂ {a,{b, c}}(vi) {a, b} ⊂ {a,{b, c}}(vii) ϕ {a, b}(viii) ϕ ⊂ {a, b, c}(ix) {x: x + 3 = 3}= ϕ
Answer» (i) This is not subset of given set but belongs to the given set. Thus, the correct form would be a ∈ {a,b,c} (ii) In this {a} is subset of {a, b, c} Thus, the correct form would be {a} ⊂ {a, b, c} (iii) ‘a’ is not the element of the set. So, the correct form would be {a} ∈ {{a}, b} (iv) {a} is not a subset of given set. So, the correct form would be {a} ∈ {{a}, b} (v) {b, c} is not a subset of given set. But it belongs to the given set. Thus, the correct form would be {b, c} ∈ {a,{b, c}} (vi) {a, b} is not a subset of given set. Thus, the correct form would be {a, b}⊄{a,{b, c}} (vii) ϕ does not belong to the given set but it is subset. Thus, the correct form would be ϕ ⊂ {a, b} (viii) Since, it is the correct form. ϕ is subset of every set. (ix) x + 3 = 3 x = 0 = {0} It is not ϕ Thus, the correct form would be {x: x + 3 = 3} ≠ ϕ

Which of the following statements are correct? Write a correct form of each of the incorrect statements.(i) a ⊂ {a, b, c}(ii) {a} {a, b, c}(iii) a {{a}, b}(iv) {a} ⊂ {{a}, b}(v) {b, c} ⊂ {a,{b, c}}(vi) {a, b} ⊂ {a,{b, c}}(vii) ϕ {a, b}(viii) ϕ ⊂ {a, b, c}(ix) {x: x + 3 = 3}= ϕ

Answer»

(i) This is not subset of given set but belongs to the given set.

Thus, the correct form would be

a ∈ {a,b,c}

(ii) In this {a} is subset of {a, b, c}

Thus, the correct form would be

{a} ⊂ {a, b, c}

(iii) ‘a’ is not the element of the set.

So, the correct form would be

{a} ∈ {{a}, b}

(iv) {a} is not a subset of given set.

So, the correct form would be

{a} ∈ {{a}, b}

(v) {b, c} is not a subset of given set. But it belongs to the given set.

Thus, the correct form would be

{b, c} ∈ {a,{b, c}}

(vi) {a, b} is not a subset of given set.

Thus, the correct form would be

{a, b}⊄{a,{b, c}}

(vii) ϕ does not belong to the given set but it is subset.

Thus, the correct form would be

ϕ ⊂ {a, b}

(viii) Since, it is the correct form. ϕ is subset of every set.

(ix) x + 3 = 3

x = 0 = {0}

It is not ϕ

Thus, the correct form would be

{x: x + 3 = 3} ≠ ϕ