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 1

(i) False

Since, {c, d} is not a subset of A but it belong to A.

Hence, {c, d} ∈ A

(ii) True

Thus, {c, d} ∈ A

(iii) True

Since, {c, d} is a subset of A.

(iv) Here, it is true that a belongs to A.

(v) False

Here, a is not a subset of A but it belongs to A

(vi) True

Thus, {a, b, e} is a subset of A.

(vii) False

Since, {a, b, e} does not belong to A, {a, b, e} ⊂ A this is the correct form.

(viii) False

Here, {a, b, c} is not a subset of A

(ix) False

Since, ϕ is a subset of A.

Hence, ϕ ⊂ A.

(x) False

Hence, {ϕ} is not subset of A, ϕ is a subset of A.