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

Question

C = {x│x≥1}

D = {x│x>9}

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

Answer 1

Hi, Maria.

So, we know C = {xΙ x≥1}

and D = {x l x>9}

So, C ∪ D is C union D, which includes everything in both sets.

So, since C includes 1 and every real number greater than one and D includes all real numbers greater than 9, then their union would include all real numbers greater than and including 1. This is written as:

C ∪ D = [1,+∞)

And C ∩ D is the intersection of the two sets which are the real numbers that both sets have in common.

C ∩ D = (9,+∞)

because both sets include all real numbers greater than (but not equal to) 9.