B and C are sets of real numbers defined as follows.

Question

B= {z│z < 4}

C= {z│z ≤ 9}

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

Answer 1

Greetings! Lets solve this shall we ?

So, we must translate the given sets into interval notation. Now, we must specify what the intervals are for B U C and B ∩ C such that the set B is

B = { z | z < 4} where the interval notation for this is (-∞, 4) and the interval notation for set C is

C = {z | z ≤ 9} where the interval notation for this is (-∞, 9].

B intersection C: B ∩ C = (-∞, 4) since this interval is also located in the set C.

B union C: B U C = (-∞, 4) U (4, 9] since we have to unite both intervals into one.

I hope this helped!

Answer 2

B is the set of all integers which are strictly less than 4 (-∞, 4)

C is the set of all integers which are less than or equal to 9 (-∞, 9]

B U C includes all elements in both set B then C, hence B U C = (-∞, 9] = C

B ∩ C includes all elements which are in B and C simultaneously, hence B ∩ C = (-∞, 4) = B