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dalvyx [7]
3 years ago
11

Arrange the given steps in the correct order to find A and B if A and B are two sets where A – B = {1, 5, 7, 8}, B – A = {2, 10}

and A ∩ B = {3, 6, 9}.
Mathematics
1 answer:
GarryVolchara [31]3 years ago
5 0

Answer:

A = {1, 3, 5, 6, 7, 8, 9}

B = {2, 3, 6, 9, 10}

Step-by-step explanation:

Here as given in the question:

A – B = {1, 5, 7, 8}   ⇒ {1, 5, 7, 8} is in A not in B.

B – A = {2, 10} ⇒  {2, 10} is in B  not in A

A ∩ B = {3, 6, 9}   ⇒ {3, 6, 9} is BOTH in A and B.

Step 1:

Set A can also be expressed as :  A = (A - B) ∪ (A ∩ B)

Set A can also be expressed as :  B = (B - A) ∪ (A ∩ B)

Step 2:

Substituting the values of (A - B) and (B - A)

A = {1, 5, 7, 8} ∪ {3, 6, 9}

B = {2, 10} ∪ {3, 6, 9}.

Step 3:

Finding the UNION of the above two sets, we get:

A = {1, 3, 5, 6, 7, 8, 9}

B = {2, 3, 6, 9, 10}

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<h3>Answer:  Choice A) 252 in^2</h3>

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Explanation:

Refer to the diagram below.

The red rectangle is 6 inches by 12 inches, so its area is 6*12 = 72 square inches. There are two of these rectangles (one on top, one on the bottom). That accounts for 2*72 = 144 square inches so far.

The purple rectangles are 3 inches by 12 inches, yielding an area of 3*12 = 36 square inches each. That's another 2*36 = 72 square inches when we account for the front and back purple rectangles.

The green rectangles are 6 inches by 3 inches. Each green rectangle is 6*3 = 18 square inches. Having two of them means we'll add on 2*18 = 36 square inches.

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-------------------------

Alternative Method:

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SA = 2*(L*W + L*H + W*H)

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SA = 2*(126)

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So we get the same answer either way

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3 years ago
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