How many elements has P(A), if A = ϕ ?

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?

(i) {3, 4} ⊂ A

(ii) {3, 4} ∈ A

(iii) {{3, 4}} ⊂ A

(iv) 1 ∈ A

(v) 1 ⊂ A

(vi) {1, 2, 5} ⊂ A

(vii) {1, 2, 5} ∈ A

(viii) {1, 2, 3} ⊂ A

(ix) ϕ ∈ A

(x) ϕ ⊂ A

(xi) {ϕ } ⊂ A

Write down all the subsets of the following sets:

(i) {a}

(ii) {a, b}

(iii) {1, 2, 3}

(iv) ϕ

Write the following as intervals:

(i) {x: x ∈ R, – 4 < x ≤ 6}

(ii) {x : x ∈ R, – 12 < x < –10}

(iii) {x: x ∈ R, 0 ≤ x < 7}

(iv) {x : x ∈ R, 3 ≤ x ≤ 4}

Write the following intervals in set-builder form:

(i) (– 3, 0)

(ii) [6, 12]

(iii) (6, 12]

(iv) [–23, 5)