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

Question

F= {x│x < 3}

H= {x│x ≥ 7}

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

Answer 1

F is all numbers less than 3.

H is all numbers greater than or equal to 7.

F U H is a union of sets F and H. It means, we take all numbers from the F set and all the numbers from the H set. Therefore, the answer to F U H is all numbers less than 3 and all numbers greater than or equal to 7. As intervals, this is expressed as (-∞,3) U [7,∞).

A round bracket indicates that the endpoint is not included, and a square bracket indicates that the endpoint is included. 3 is excluded because it is a strict inequality (strictly less than 3), and infinities are excluded because for any theoretical number we choose to represent positive/negative infinity there are infinitely many larger/smaller numbers.

F ∩ H means an intersection of sets F and H: a set that contains only elements that belong to both. As these sets do not overlap, F ∩ H is Ø.