1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Which of the following statements are true ? Give 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.

Open in App
Solution

## (i) False, because the two sets A and B need to be comparable. (ii) False, because {1} is a finite subset of the ifinite set N of natural numbers. (iii) True, because the order (or cardinal number) of any subset of a set is less than or equal to the order of the set. {order (or cardinal number) of a set is the number of elements in the set}. (iv) False , because the empty set ϕ has no proper subset. (v) False, because {a, b, a, b,.....} = {a, b} (repetition is not allowed) ∴ {a, b, a, b,....} is a finite set. (vi) True, ∵ equivalent sets have the same cardinal number. (vii) False, One knows that if the cardinal number of a set A is n, then the power set of A denoted by P(A) which is the set of all subsets of a, has the cardinal number 2n. If the cardinal number of A is infinite, then the cardinal of P(A) is also infinite. Hence, the above statement is true provided the set is infinite.

Suggest Corrections
11
Join BYJU'S Learning Program
Related Videos
Finite and Infinite Set
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program