Question

What is the solution set of x n x ?

a. all numbers less than -5 and greater than 5
b. the numbers between -5 and 5
c. the empty set
d. all real numbers

Answer 1

The solution set empty set or null set ⇒ answer c

Explanation:

* Lets study the meaning of the inequality

- If a < x < b, that means the value of x is between a and b

- If a ≤ x ≤ b, that means the value of x is from a to b

- If x < a and x > b, that means the value of x is smaller than a and

grater than b

- If x ≤ a and x ≥ b, that means the value of x is smaller than or equal a and

grater than or equal b

* Now lets solve the problem

∵ {x I x < -5}

∴ x is smaller than -5

∵ {x I x > 5}

∴ x is greater than 5

∵ {x I x < -5} ∩ {x I x > 5}

- The meaning of ∩ is the common numbers between the

two sets, but there is no common numbers between the

two sets

∴ {x I x < -5} ∩ {x I x > 5} = { }

∴ The solution set empty set or null set

Answer 2

c. the empty set

Explanation:

set of x < - 5 n x

The set x < - 5 comprises of real numbers that are less than -5;

(-6, -7, -8, -9, -10, -11, ......)

On the other hand, the set x > 5 comprises of real numbers greater than 5;

(6, 7, 8, 9, 10, 11, ......)

Clearly, the intersection of the above sets is empty, in that the intersection has no elements.

Therefore, x < - 5 n x is an empty or null set