Answer:
Step-by-step explanation:
The symbols of interest here are ...
∪ -- union. Everything that is in either of the sets.
∩ -- intersection. Everything that is in both of the sets.
superscript C -- complement. Everything that is not in the set. An apostrophe (') can also be used to signify the complement.
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(a) A∩B∩C'
In the first attachment, set A is all of the sections marked 2, 3, 5, 6. Set B is all of the sections marked 3, 4, 5, 7. The sections in both sets are where the circles for A and B overlap:
A∩B = {3, 5}
The sections that are not in set C are 1, 2, 3, 4. So, the one section that is in A∩B, but outside C is section 3.
The checked section is shown in the second attachment.
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(b) A'∩B∩C
In the first attachment, set A' is all of the sections marked 1, 4, 7, 8. These are all of the sections not in set A. The ones of these that are also in set B are 4 and 7. And the one of these that is also in set C is section 7.
The checked section is shown in the third attachment.
So for this, I will be doing the elimination method. Firstly, multiply both sides of the first equation by 2:
Next, add the two equations together to get . From here you can solve for x.
For this equation, just divide both sides by 8 and your first answer will be
Now that we have the value of x, substitute it into either equation to solve for y:
<u>In short, the solution is (2,-5), or A.</u>
