URGENT! need help with algebra question asap!

Question

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

E= {v | v  ≤ 4}

F= {v | v < 9}

Write E ∪ F and E ∩ F using interval notation.

Answer 1

E is all the real numbers less than or equal to 4.

F is all the real numbers less than but NOT equal to 9

The union (∪) Is the set of numbers if you combine both sets E and F. Notice that F, which is all numbers less than 9, includes all the numbers less than or equal to 4, all the numbers in E. In math terms, F is a superset of E. So the answer is just set F.

In interval notation: (∞,9)

Parenthesis on the 9 because it is not included.

The intersection (∩) is all the numbers included in both sets E and F. Looking at both sets, notice that set E is all the number up until and including 4. The rest of the numbers up until 9 is in set F, but not set E, so these are not in the intersection. So our answer is only set E.

In interval notation: (∞,4]

Notice square brackets this time because 4 is included. Infinite always is not included and uses parenthesis.