Question 1196537: Let U = {q, r, s, t, u, v, w, x, y, z}, A = {q, s, u, w, y}, B = {q, s, y, z}, and C = {v, w, x, y, z}. List the elements in the following set.
A ∩ B with line on top
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
A ∩ B with line on top
First, A ∩ B is equal to the set that contains elements common to both A and B. The line on top means “complement” (all the objects that do not belong to set A∩ B), and you can write it as (A ∩ B)’ or (A ∩ B)^c
to find (A ∩ B)’ , first find A ∩ B (elements common to both A and B)
if A = {q, s, u, w, y} and B = {q, s, y, z}
A ∩ B={q, s, y}
now find complement (A ∩ B)’ (all the objects in set U that do not belong to set A∩ B)
(A ∩ B)’={ r, t, u, v, w, x, z} => your answer
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
There's ambiguity when you mention "with a line on top"
Is the line solely over the B? Or is it over everything?
Do you mean 
Or do you mean 
---------------------------------------------------------------------
I'll go over each interpretation.
Let's focus on
The universal set is
U = {q, r, s, t, u, v, w, x, y, z}
Cross off the stuff you find in set B
So we'll cross off: q, s, y, and z
This forms the set B' which is the same as writing 
B' = {r, t, u, v, w, x}
This is the complement of set B.
Stuff in B' is not found in B, and vice versa.
They are complete opposite of one another.
The two sets union together to form the universal set.
Think of it like this:
stuff inside B is inside a house
stuff outside B is outside the house
Now we'll intersect the set A with set B'
A = {q, s, u, w, y}
B' = {r, t, u, v, w, x}
We see that the letters u and w are inside both A and B' at the same time.
Hence A ∩ B' = {u, w}
which is the same as saying 
-----------------------------------------------------
Now onto
This is the same as writing (A ∩ B)'
We're taking the complement of set (A ∩ B)
Here are sets A and B
A = {q, s, u, w, y}
B = {q, s, y, z}
which means,
A ∩ B = {q, s, y}
since those three letters are found in both sets
We'll delete q,s,y from the universal set
U = {q, r, s, t, u, v, w, x, y, z}
(A ∩ B)' = {q, r, s, t, u, v, w, x, y, z}
(A ∩ B)' = {r, t, u, v, w, x, z}
Therefore, 
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