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Question -

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 isn’t subset of given set but belongs to the given set.
∴ The correct form would be
a ∈{a,b,c}
(ii) In this {a} is subset of {a, b, c}
∴ The correct form would be
{a} ⊂ {a, b, c}
(iii) ‘a’ is not the element of the set.
∴ The correct form would be
{a} ∈ {{a}, b}
(iv) {a} is not a subset of given set.
∴ 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.
∴ The correct form would be
{b, c} ∈ {a,{b, c}}
(vi) {a, b} is not a subset of given set.
∴ The correct form would be
{a, b}⊄{a,{b, c}}
(vii) ϕ does not belong to the given set but it is subset.
∴ The correct form would be
ϕ ⊂ {a, b}
(viii) It is the correct form. ϕ is subset of every set.
(ix) x + 3 = 3
x = 0 = {0}
It is not ϕ
∴ The correct form would be
{x: x + 3 = 3} ≠ ϕ

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