Question

If U = {1,2,3,4,5,6,7,8,9, l0} and
A = {1,2,3}
B = {2,4,6,8}
C = {7,8,9,10}
Find the following:
a. A′
b. (A U B)
c. (A′ ∩ B)′

Answer 1

A', is the set of all element in the universal set U, but not in the set A.

Answer 2

A∪B, is the set of all elements in either A or B.

Answer 3

What would the answers be? Is A' = 1,2,3,4,5,6,7,8,9,10?

Answer 4

no, 1,2,3 are in A

Answer 5

oh wait, it would be 4,5,6,7,8,9,10

Answer 6

that's better.

Answer 7

So (AUB) = 1,2,3,4,6,8?

Answer 8

yep

Answer 9

Now for the last one

(A′ ∩ B), is the set all elements in both A' and B.

(A′ ∩ B)′, is the set of all elements in the universal set U, but not in (A′ ∩ B).

Answer 10

So (A' and B') = 123?

Answer 11

find (A′ ∩ B) first

Answer 12

there should not be any `B'`

Answer 13

(a' union b) is {2,4,5,6,7,8,9,10)

Answer 14

\(\cap\) is the intersection, (not the union)

Answer 15

whats the answer for the last one?

Answer 16

(A′ ∩ B)

= {4,5,6,7,8,9,10} ∩ {2,4,6,8}
=

Answer 17

So (a' intersection b)' = 4,6,8

Answer 18

No,
(A′ ∩ B) = {4,6,8}


Now find
(A′ ∩ B)′

Answer 19

how do I find that?

Answer 20

(A′ ∩ B)′

= U \ (A′ ∩ B)

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} \ {4, 6, 8}

(where \ is setminus)

Answer 21

so that's that answer?

Answer 22

no, simplify

Answer 23

take the elements 4,6,8, from the universal set

Answer 24

then what

Answer 25

then you will have the answer to c.

Answer 26

so its (1,2,3,5,7,9,10) / (4,6,8)?

Answer 27

perform the setminus operation

Answer 28

can you just give me the answer? I don't understand.

Answer 29

for example

{0, 15, 18, 100, 458} \ {18,100}

= {0, 15, 458}

Answer 30

so its 1, 2, 3, 5, 7, 9,10?

Answer 31

that's right.

but don't forget to write the braces around the elements of a set

(A′ ∩ B)′ = {1, 2, 3, 5, 7, 9, 10}

Answer 32

thank you!