Give one example each for a finite set and an infinite set.

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Solution

If $A$ is a set of natural numbers less than $10$ , i.e.,
$A = {x : x < 10, x \in N}$
$A$ is an example of finite set.
If $B$ is a set of all natural numbers, i.e.,
$B = {x : x \in N}$
$B$ is an example of infinite set.

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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.

r

A_{r} = {e^{i π r n} : n is a natural number}

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