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
{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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