The U looking symbol between the "A" and "B" means "union". This is basically a shorthand symbol that tells us "combine the two sets A and B to form one giant set (toss out duplicates)"
The U in U = {1, 2, 3, 4, 5, 6, 7} looks almost identical to the union symbol. It's unfortunate that this similar type of symbol shows up twice. To avoid confusion, I'm going to use the letter U to mean "union" and the letter V to mean "universal set". In other words, I'm changing
U = {1, 2, 3, 4, 5, 6, 7}
to
V = {1, 2, 3, 4, 5, 6, 7}
that way we don't have overlapping symbols
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So we have these two given sets
A = {2, 5, 6, 7}
B = {1, 6, 7}
Which combine to
A u B = {2,5,6,7 1,6,7}
the space between the values indicates where one set ends and the other begins
Sort the values from smallest to largest.
Toss out the duplicates (the extra 6 and 7)
So we end up with this set after doing so
A u B = {1, 2, 5, 6, 7}
We've effectively added the value '1' to set A
Let's call this set C, so C = A u B = {1, 2, 5, 6, 7}
Or in short, C = {1, 2, 5, 6, 7}
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Compare the two sets V and C
V = {1, 2, 3, 4, 5, 6, 7}
C = {1, 2, 5, 6, 7}
If we line up the terms, we have
V = {1, 2, 3, 4, 5, 6, 7}
C = {1, 2, X, X, 5, 6, 7}
where the X represents just an empty placeholder so that we can line things up properly
I'm going to use a red pen to cross off the values that are found in set C. See the attached image. Notice how I'm crossing off 1, 2, 5, 6 and 7 in both lists
What's left over is 3 and 4
Effectively what happened is that we started with the universal set and kicked out everything that is found in set A u B.
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So the final answer is (A u B)' = {3, 4}
Meaning you'll simply type "3,4" without quotes into the box for choice A
There is no need to type in curly braces as that is already done for you.
The answer cannot be choice B as {3, 4} is not the empty set.
