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Radda [10]
4 years ago
5

g Consider the following statement. For all sets A and B, (A − B) ∪ (A ∩ B) = A. Construct an algebraic proof for the statement.

Cite a property from Theorem 6.2.2 for every step.
Mathematics
1 answer:
umka21 [38]4 years ago
6 0

Answer:

(A − B) ∪ (A ∩ B) = A

Step-by-step explanation:

we will use below conditions

Let A and B be the two sets

<u>Distributive property</u>:-

i) A U (B ∩ C) =( AUB)∩(AUC)

ii) A ∩ (BUC) = (A ∩ B) U (A ∩ C)

we will use another conditions also iii)  A-B =A ∩ B¹

now Given (A − B) ∪ (A ∩ B) = (A ∩ B¹) ∪ (A ∩ B) ( from (iii)

                                             = A ∩ (BUB¹)   ( from (ii)

                                             = A ∩ U ( see the diagram)

                                             = A

∴ (A − B) ∪ (A ∩ B) = A

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Answer:

C is the answer.

Step-by-step explanation:

What you do is you plug the numbers in to the equation according to the x and y.

So we will solve for y.

(3, 6) and (1, -2) is what you will be using. The 3 and 1 are the x and the 6 and -2 are the y.

So lets look at number C. y-2=4(x+1). You will add an x number into the x like this. y-2=4(3+1). You will then do the distributive property to get y-2=12+4.

You will then add 12 and 4 together to get y-2=16. You will then take the 2 and add it to the 16. to get y=18.

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4 years ago
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Answer:

1. 0

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Answer:

Step-by-step explanation:

I don't see the choices, but I will make the equations that seems to be correct to me.

Known facts:

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