Question

3. Let​U = {a, c, d, f, h, m, p, r, t, w}
​​A = {a, c, f, r, t}
​​B = {a, c, m, t}
​​C = {d, m, p, r, t}

​Find:

a) (A' ∩ B) ∪ (A' ∩ C')
b) (A ∩ B ∩ C)'
c) (B ∪ C)' ∩ A
d) n (A)
e) n (A ∪ B)

Answer 1

U = universe?

Answer 2

Yeppers

Answer 3

so what is A`? and what elements does it share with B?

Answer 4

A,c,f,r,t

Answer 5

A = {c,f,r,t} so A` is all the elements of the universe that are not in A
so A` = U - A

Answer 6

d h m p w

Answer 7

?

Answer 8

right this is A` so now we need the elements that are both in A` and B

Answer 9

M

Answer 10

m yes

Answer 11

now you know A` so find C` (hint: C` = U - C )
then find the elements those two sets(A` and C` ) share.

Answer 12

A c f h w is c'

Answer 13

ok what elements does that share with A`?

Answer 14

dont use caps for elements only for sets and vice versa

Answer 15

And a' c' is h,w?

Answer 16

a` means nothing

Answer 17

A` does

Answer 18

A`C` means nothing

Answer 19

A` intercetion C` does

Answer 20

yes A` intercection C` = {h,w}

Answer 21

ok so now we have (A` intercection C`) and we have (A` intercection B` )
we need the union of these two sets, so we want every element from each set

Answer 22

intersection..sorry

Answer 23

Ok so it's (m) U (h,w) and were combining these 2?

Answer 24

{1,2,3,4,5} U {3,4,5,6,7} = {1,2,3,4,5,6,7} so its any element that is in either set
so you have {h,m,w}

Answer 25

notice if they both have the same element we only list that one once(no elements repeat in a set)