Give example of sets $A$ and $B$ such that $A$ is finite, $B$ is infinite, $A$ and $B$ are disjoint sets.

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Solution

Suppose $A =$ { $1, 3, 5, 7$ } which is a finite set
And $B$ be the set of even numbers such as { $2, 4, 6, 8......$ }
Both are disjoint sets as they do not have an element in common.

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Let A and B be two finite disjoint sets such that n(A U B) = 475 and n(A) = 435, then n(B) is

A \subseteq B or B \subseteq A;

Which of the following statements are true ? Give reason to support your answer.

(i) For any two sets A and B either A $\subseteq$ B or B $\subseteq$ 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.

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