Question

State which of the following sets are finite or infinite.
(i) {x:x belongs to N and (x - 1) (x - 2) =0}
(ii) {x:x belongs to N x²=4}
(iii) {x:x belongs to N and 2x -2=0}
(iv) {x:x belongs to N and x is prime}
(v) {x:x belongs to N and x is odd}​

Answer 1

$\huge{\underline{\underline{\red{\bold{Solution:}}}}}$

#1

☞ {x:x belongs to N and (x-1)(x-2) = 0}

• Finite Set

A = {1,2}

Here, the given equation satisfies if and only if x is equals to 1 & 2.

Check:-

Let x = 1

(1-1)(1-2) = 0

0(-1) = 0

0 = 0

Let x = 2

(2-1)(2-2) = 0

(1)0 = 0

0 = 0

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#2

{x:x belongs to N, x² = 4}

• Finite Set

A = {2}

Here, the given equation satisfies if and only if x is equals to 2

Check:-

${x}^{2} = 4 \\ x = \sqrt{4} \\ x = \sqrt{ {(2})^{2} } \\ x = 2$

--------☠-------

#3

{x:x belongs to N and 2x-2 = 0}

• Finite Set

A = {1}

Here, the given equation satisfies if and only if x is equals to 1

Check:-

2(1)-2 = 0

2-2 = 0

0 = 0

--------☠--------

#4

{x:x belongs to N and x is Prime}

• Infinite Set

A = {2,3,5,7,11,13...}

---------☠--------

#5

{x:x belongs to N and x is odd}

• Infinite Set

A = {1,3,5,7,9...}

$\Large{\tt{@MrMonarque}}$

Hopes It Requires!!

Answer 2

$\huge\sf\red{Solution:-}$

(i) {x:x belongs to N and (x - 1) (x - 2) =0}

❥︎Value of x is 1 or 2.

So the set is {1,2}.

Hence, it is finite.

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(ii) {x:x belongs to N x²=4}

❥︎x²=4

x=±2

But x belongs to N or x is a natural number.

So the set is {2}.

Hence, it is finite.

✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵

(iii) {x:x belongs to N and 2x -2=0}

❥︎In the given set x=1 and 1 belongs to N.

Hence, it is finite.

✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵

(iv) {x:x belongs to N and x is prime}

❥︎The given set is a set of all prime numbers.

There are infinitely many prime numbers.

Hence, it is infinite.

✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵

(v) {x:x belongs to N and x is odd}

❥︎Since there are infinite number of off numbers.

Hence, it is infinite.

✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵