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in Sets, Relations and Functions by (51.9k points)

Which of the following statements are true? Give a reason to support your answer.
(i) For any two sets A and B either A B or B A.
(ii) Every subset of an infinite set is infinite.
(iii) Every subset of a finite set is finite.
(iv) Every set has a proper subset.
(v) {a, b, a, b, a, b,….} is an infinite set.
(vi) {a, b, c} and {1, 2, 3} are equivalent sets.
(vii) A set can have infinitely many subsets.

1 Answer

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(i) False

No, it is not necessary for the any two set A and B to be either A B or B A.


(ii) False

Here, A = {1,2,3} It is the finite subset of infinite set N of natural numbers.


(iii) True

The logically smaller part of something finite can never be infinite.

Therefore, every subset of a finite set is finite.


(iv) False

Since, null set or empty set does not have a proper subset.


(v) False

We do not repeat elements in a set, therefore the given set becomes {a, b} which is a finite set.


(vi) True

The equivalent sets have same number of elements.


(vii) False

In A = {1}

Hence, the subsets can be ϕ and {1} which are finite.

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