If A = {1} and B = {{1}, 2} then show that A ⊄ B.

Hint 1 ϵ A but 1⊄ B.

State in each case whether A ⊂ B or A ⊄ B.

A = {x : x is an even natural number less than 8}, B = {x : x is a natural number which divides 32}

Examine whether the following statements are true of false:

(i) {a, b} ⊄{b, c, a}

(ii) {a}ϵ {a, b, c}

(iii) ϕ ⊂{a, b, c}

(iv) {a, e} ⊂{x : x is a vowel in the English alphabet}

(v) {x : x ϵ W, x + 5 = 5} =ϕ

(vi) a ϵ {{a}, b}

(vii) {a} ⊂ {{a}, b}

(viii) {b, c} ⊂{a, {b, c}}

(ix) {a, a, b, b} = {a, b}

(x) {a, b, a, b, a, b, ….} is an infinite set.

(xi) If A = set of all circles of unit radius in a plane and B = set of all circles in the same plane then A⊂B.

Write down all subsets of each of the following sets:

(i) A = {A}

(ii) B = {a, b}

(iii) C = {–2, 3}

(iv) D = {–1, 0, 1}

(v) E =ϕ

(vi) F = {2, {3}}

(vii) G = {3, 4, {5, 6}}

Express each of the following sets as an interval:

(i) A = {x : x ϵR, –4 < x < 0}

(ii) B = {x : x ϵ R, 0 ≤ x < 3}

(iii) C = {x : x ϵ R, 2 < x ≤ 6}

(iv) D = {x : x ϵ R, –5 ≤ x ≤ 2}

(v) E = {x : x ϵ R, –3 ≤ x < 2}

(vi) F = {x : x ϵ R, –2 ≤ x < 0}