E and F are sets of real numbers defined as follows.

Question

E = {w│w<4}

F = {w│w≥4}

Write E U F and E ∩ F using interval notation. If the set is empty, write Ø

Answer 1

E ∪ F in interval notation is (-∞,∞).

The union of the two sets means it includes every value less than 4, equal to 4, and greater than 4.

E ∩ F is ∅

This is asking for the intersection of the two sets. However, one set includes all values less than 4 while the other set includes values 4 and greater. There is no overlap of values in the two sets, therefore the set is null, or ∅.

Answer 2

E ∪ F = the set of all numbers that are in E or in F or in both E and F = (-∞, ∞)

E ∩ F = the set of all numbers that are in both of E and F = ∅