How can I identify the union and intersection of these sets containing geometric shapes?

.A)If A={Parallelograms}

B={Rectangles}

C={Squares}

Simplify the following,and describe why?

a) A union B

b) B intersect C

c) A intersect C

B)If U={all tringles}

A={Obtuse angle triangle}

B={Right angle Triangle}

C={Issosceles triangle}

and D is another set such that D subset of C, D ontersect A={O} and D intersect B={O}.

What does D represent?

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a) A union B. The answer to this would be all of both groups because it is a "union." Specifically, the answer would be all parallelograms and all rectangles. Technically, this is a duplication because all rectangles are parallelograms. Therefore, it would be more correct to say "all parallelograms."

b) B intersect C Since this is an "intersection" it would only be those items that are members of both groups B and C. If something is a member of one of the groups and not the other, it would not be included. The answer, therefore is "squares." This is because squares are the only shapes that are both rectangles and squares.

c) A intersect C The answer to this question would also be "squares." We are looking for the shapes that are both parallelograms and squares. Since all squares are also parallelograms, all squares satisfy this condition.

For the second problem, the answer is "acute isosceles triangles." Using this group as D, it meets the stated conditions:

D is a subset of C - acute isosceles triangles are a specific type of isosceles triangles so it would be a subset of the larger isosceles triangles group

There are no items in the intersection between D and A. By definition, "acute" isosceles triangles can never be obtuse. (Acute means that the largest angle is less than 90 whereas obtuse means the largest angle is greater than 90.)

There are no items int he intersection between D and B. By definition. "acute" isosceles triangles have their largest angle less than 90 where as "right" triangles have an angle that is 90. So, no triangles would be in both grouops.

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