Find sets of A and B

Question

A= {vIv<=1 } B= {vlv <6} Write A U B and A ∩ B using interval notation. If the set is empty, write ∅

Answer 1

Greetings! Lets solve this shall we ?

So, we must find out the sets A U B and A ∩ B given that

A = {v I v ≤ 1 } and B = {v l v < 6}

The set A in interval notation is represented as A = (-∞, 1] and set B is represented as B = (-∞, 6). Now lets find A U B first. We combine both sets for union such that

A U B = (-∞, 1] U [1, 6), since 6 is not included because of the strictly greater than sign. Now lets find A intersection B such that

A ∩ B = (-∞, 1], since the interval (-∞, 1] is also in set B.

I hope this helped!