What is the solution set of [x1x< -5) n {x1x > 5)?
all numbers less than -5 and greater than 5
the numbers between -5 and 5
the empty set
all real numbers

  the empty set

Step-by-step explanation:

The solution to {x | x < -5} is all numbers less than -5.

The solution to {x | x > 5} is all numbers greater than 5.

The solution to the intersection of these sets is ...

There are no numbers that are both less than -5 and greater than 5. That description is just a wordy way to say "the empty set."

Comment on the notation

The vertical bar symbol (|) used in these set-builder descriptions is not a 1 (one) or l (ell) or I (eye). It can be replaced with a colon (:) and the meaning is exactly the same.

  {x | x < -5} . . . is read "the set of all x such that x is less than minus five"

The notation

  {x : x < -5} . . . is read exactly the same way.

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The upside-down U is ∩, the symbol for "intersection". It effectively means "and" in that the result of the intersection of two sets is the set of those elements that are in one set and the other set.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

step-by-step explanation: