Question 148102This question is from textbook A Survey Mathematics with Applications
: I'm just learning how to do these and need a little help please?
pts) Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set
a) A ∩ B
b) A ∩ C
c) A U C
d) B U C
e) (A U B) ∩ C
f) A U (B U C)
g) (A ∩ B) ∩ C
h) (A ∩ B) U C
This question is from textbook A Survey Mathematics with Applications
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set
.
∩ - intersection of two sets -- elements that are in common
U - union of two sets -- combines the elements of both sets together
.
a) A ∩ B
List all elements that are common between A and B:
{3}
.
b) A ∩ C
List all elements that are common between A and C:
{3}
.
c) A U C
List of elements in both A and C:
{1, 2, 3, 5, 7}
.
d) B U C
List of elements in both B and C:
{3, 4, 5, 6, 7}
.
e) (A U B) ∩ C
We first do (A U B) which is:
{1, 2, 3, 4, 5, 6,}
Then:
{1, 2, 3, 4, 5, 6,} ∩ C
{1, 2, 3, 4, 5, 6,} ∩ {3, 5, 7}
{3, 5}
.
f) A U (B U C)
First do (B U C) which is:
{3, 4, 5, 6, 7}
then:
A U {3, 4, 5, 6, 7}
{1, 2, 3} U {3, 4, 5, 6, 7}
{1, 2, 3, 4, 5, 6, 7}
.
g) (A ∩ B) ∩ C
First do (A ∩ B):
{3}
then:{3} ∩ C
{3} ∩ {3, 5, 7}
{3}
.
h) (A ∩ B) U C
First do (A ∩ B) which is:
{3}
then:{3} U C
{3} U {3, 5, 7}
{3, 5, 7}
.
|
|
|
