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Finite and Infinite Set

State, which ...

Question

State, which of the following sets are finite and which are infinite:
$B = {x : x \in W a n d 5 x - 3 \leq 20}$

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Solution

Given $5 x - 3 \leq 20$
Adding 3 to both sides, we get
$\to 5 x - 3 + 3 \leq 10 + 3 \to 5 x \leq 23$
Dividing both sides by 5, we get
$x \leq \frac{23}{5} \to x \leq 4.6 ∴ B = {0, 1, 2, 3, 4}$
We know that a set with finite number of elements is called a finite set.
$B = {x : x \in W a n d 5 x - 3 \leq 20}$ is a finite set.

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Similar questions

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.

(i) A = {x : x \in Z : x

}

(i i) B = {x : x \in R :< - 10}

A =

x : x

x \in N

B =

x : x

(i) A = {x : x \in Z : x^{2}

}

(i i) B = {x : x \in R : - 4 < x < - 2}

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