# Thread: Intersection, Union, and Compliment of sets

1. ## Intersection, Union, and Compliment of sets

Let U={1,2,3,4,5,6,7,8,9}, A={3,4,5,6,8}, B={2,4,7,8,9}, C={4,5,6,7,8} and find:

a. A∩B b. A∪C c. A' d. B'∩A' e. AU(B∩C) f.A∩(BUC) g. {(A∩B') U (A∩B)}' h. (A'UB'UC)'

2. a. A∩B={4,8}
b.AUC={3,4,5,6,7,8}
e.AU(BnC)=AU{4,7,8}={3,4,5,6,7,8}
f. An(BUC)=An{2,4,5,6,7,8}={4,6,8}

Where does the ' stand for? For the complement?

my apologies if there are some mistakes, i did it quickly

3. Kuntah:

The ' denotes the complement of the set. Since U is given, but not explicitly stated in the questions I assumed that it was the complement with respect to U. e.g. in set difference notation A'=U\A= {1,2,7,9} Can you do the rest now?

also f.) $A\cap(B\cup C) = \{3,4,5,6,8\}\cap\{2,4,5,6,7,8,9\}=\{4,5,6,8\}$

4. I think you will find these questions amazingly simple, if you read what the symbols mean.

intersection: the set containing elements common to both sets
union: the set of elements contained by both sets (counting similar elements only once)
Complement: The elements belonging to U that do not belong to A written U\A or just A' if there is no ambiguity.

It's so easy try it

5. c. A'={1,2,7,9}
d.B'nA'={1,3,5,6}n{1,2,7,9}={1}
g.{({3,4,5,6,8}n{1,3,5,6})U({4,8})}'={3,5,6,4,8}'= {1,2,7,9}
h.({1,2,7,9}U{1,3,5}U{4,5,6,7,8})'={1,2,3,4,5,6,7, 8,9}'=empty set

,

,

### a compliment intersection b compliment

Click on a term to search for related topics.