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Question -

Let A = {a, b,{c, d}, e}. Which of the following statements are false and why?
(i) {c, d} ⊂ A
(ii) {c, d} A
(iii) {{c, d}} ⊂ A
(iv) a A
(v) a ⊂ A.
(vi) {a, b, e} ⊂ A
(vii) {a, b, e} A
(viii) {a, b, c} ⊂ A
(ix) ϕ A
(x) {ϕ} ⊂ A



Answer -

(i) False
{c, d} is not a subset of A but it belong to A.
{c, d} ∈ A
(ii) True
{c, d} ∈ A
(iii) True
{c, d} is a subset of A.
(iv) It is true that a belongs to A.
(v) False
a is not a subset of A but it belongs to A
(vi) True
{a, b, e} is a subset of A.
(vii) False
{a, b, e} does not belong to A, {a, b, e} ⊂ A this is the correct form.
(viii) False
{a, b, c} is not a subset of A
(ix) False
ϕ is a subset of A.
ϕ ⊂ A.
(x) False
{ϕ} is not subset of A, ϕ is a subset of A.

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