Question

Which of the following are the empty set?

1. {x | x is a real # and x2 - 1 = 0}

2. {x | x is real # and x2 + 1 = 0}

3. {x | x is a real # and x2=9}

4. { x | x is a real # and x = 2x + 1}

5. { x | x is a real # and x = x+1}

Answer 1

Heya!

Here is yr answer.....

Empty set :
~~~~~~~~~~

<> The set without elements is said to be empty set (or) Null set.

<> Empty set is denoted by 'ø' or ' { } '

Coming to yr quest....

(1) x² - 1 = 0

x = 1

=> 1² - 1 = 0

=> 1 - 1 = 0

=> 0=0

x = -1

=> (-1)² - 1 = 0

=> 1 - 1 = 0

=> 0 = 0

= { 1 , -1}


(2) x² + 1 = 0

x = 1

=> (1)² + 1 = 0

=> 1 + 1 = 0

=> 2 = 0

2 ≠ 0

x = 2

=> (2)² + 1 = 0

=> 4+1 = 0

=> 5 = 0

5 ≠ 0

We cannot find any elements for the set....

So, it is a empty set.


(3) x² = 9

x = 3

=> 3² = 9

=> 9 = 9

x = -3

=> (-3)² = 9

=> 9 = 9

= {3 , -3}

(4) x = 2x+1

x = 1

=> 2(1)+1

=> 2+1

=> 3

x = 2

=> 2(2)+1

=> 4+1

=> 5

x = 3

=> 2(3)+1

=> 6+1

=> 7


= {2,5,7......} (infinite set)


(5) x = x+1

x = 1

=> 1+1

=> 2

x = -1

=> -1+1

=> 0


x = 0

=> 0+1

=> 1

= { 2, 0 , 1.....} (infinite set)



Therefore, (2) is the empty set!





Hope it helps...

Answer 2

i think answer is 2. and 5