Question

Which of the following sets are null sets
0 A = { x | x? = 16 and 2x = 4
(i) B = {x|x + 6 = 6).​

Answer 1

Answer:

Your answer is set A.

we have,

A={x|x^2=16 and 2x=4}

here we have,

x^2=16

x=4 or -4 ---------(1)

also we have 2x=4

ie. x=4/2=2 --------(2)

thus form eq--(1) and (2),

we can conclude that , there doesn't exist any real number x such that,

x^2=16 and 2x=4 at the same time,

and hence no element is found in set A thus setA is an empty set.

now , we have,

B ={x|x+6=6}

here, if x+6=6

then ,x=6-6=0.

thus we can say that the element 0 ( zero) can exist in set B, and hence setB is not an empty set.

I hope it would help you

thank you