Examine whether the following statements are true of false:

Question:

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.

Solution:

(i) False

Explanation: Since elements of {a,b} are also elements of {b,c,a} hence {a, b}⊂{b, c, a}.

(ii) False

{a} is not in {a,b,c}. Hence, {a} ∉ {a, b, c}.

(iii) True

Explanation: ϕ is a subset of every set.

(iv) True

Explanation: a, e are vowels of English alphabet.

(v) False

Explanation: 0+5 = 5 , 0 ϵ W

Hence, {0} ≠ ϕ

(vi) False

Explanation: a is not an element of {{a}, b}

(vii) False

As a is not an element of set {{a}, b}

(viii) False

Explanation: {b,c} is an element of {a, {b, c}} and element cannot be subset of set

(ix) True

Explanation: In a set all the elements are taken as distinct. Repetition of elements in a set do not change a set.

(x) False

Explanation: Given set is {a,b}, which is finite set. In a set all the elements are taken as distinct.Repetition of elements in a set do not change a set.

(xi) True

Explanation: Circle in a plane with unit radius is subset of circle in a plane of any radius.