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.


(i) False

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


(ii) False


Explanation: {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.


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