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}
Answers
#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
---------☠---------
#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:-
--------☠-------
#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...}
Hopes It Requires!!
(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.
✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵
(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.
✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵✵