What is the solution set of {x | x < - 5} n {x | x > 5} ? 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

c. the empty set

Step-by-step explanation:

set of {x | x < - 5} n {x | x > 5}

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 | x < - 5} n {x | x > 5} is an empty or null set

The solution set empty set or null set ⇒ answer c

Step-by-step 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

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step-by-step explanation: