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0 votes
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in Sets, Relations and Functions by (51.9k points)

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

1 Answer

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Best 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

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