It is given that = {1, 2, 3, 4, 5, 6, 7, 8, 9},
Draw a Venn diagram to illustrate the given
= {1, 2}, and B = {1, 2, 3, 4].
information.
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Answers
Since they've given me three sets inside the universe, I'll draw three circles inside a box, and label them with the sets' names.
a box, being the universe; containing three overlapping circles, labelled A (upper left), B (middle right), and C (bottom left)
(They don't usually want the universe named; the box is sufficient indication. For some reason, the names on the circles whose elements are given go outside the circles, which can be confusing. Despite the drawing, there are no elements A, B, or C in this universe.)
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The set A contains the numbers 1, 2, 3, 4, 5, and 6. (These numbers are the set's elements.) The number 6 is in all three of the input sets, so this element will go in the triangle-ish central overlap area of all three circles. Also, A shares 2 and 4 with B, so these will go in the rest of the overlap of these two sets. And A shares 3 and 5 with C, so this will go in the rest of the overlap area with C. The remaining elements, being in this case just the number 1, go into the only-A part of A's circle.
6 is in the center overlap; 2 and 4 are in the overlap of just A and B; 3 and 5 are in the overlap of just A and C; 1 is in the only-A portion of A's circle
The set B shares 6 and 9 with C. (I've already handled its overlap with A.) But 6 is shared by all three sets, so I only need to put the 9 in the overlap with C. The remaining elements, being in this case just the number 8, go into the only-B part of B's circle.
9 is in the overlap of just B and C; 8 is in the only-B portion of B's circle
The set C is left and, since I've already handled the overlaps with A and B, I only need to insert the remaining elements of C, which is just the number 7. This go in the only-C portion of C's circle.
7 is in the only-C portion of C's circle
There is one number which isn't in any of the named sets. So, outside of the circles, I'll put the remaining 10.
10 is inside the box but outside all three circles
I've completed the "population" portion of this exercise. To handle the set relationships, I'll work from the inside out. I need first to find A complement C, which is A, after I've thrown out its overlap with C. This gives me:
the lune of A, formed by deleting A's overlap with C, is shaded green; the shaded portion is a set containing 1, 2, and 4
Now I have to add in all of B:
B's circle is also shaded green; the shaded portion is a set containing 1, 2, 4, 6, 8, and 9
And now I have to take the complement of this, which means that I'll flip the shading, giving me something that includes most of C and the otherwise unclaimed portion of U:
the shading is reversed; the new shaded portion is a lune of C and the rest of the universe U outside of A and B; that is, a set containing 3, 5, 7, and 10
From this diagram, I can read off the new set created by the set-relation expression they gave me:
\footnotesize{\mathbf{\color{purple}{ \textbf{\normalsize{[}}\textbf{(}A - C\textbf{)} \cup B\textbf{\normalsize{]}}^{\complement} = \textbf{\{}3, 5, 7, 10\textbf{\}} }}}[(A−C)∪B]
∁
={3,5,7,10}
Answer:Assalamualaikum.Ok, she will be fine don't worry we are praying to Allah for her
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