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}

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

A = {x : x is a square in a plane}, B = {x : x is a rectangle in the same plane}

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

A = {x : x is a triangle in a plane}, B = {x : x is a rectangle in the same plane}

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.

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

Hint 1 ϵ A but 1⊄ B.