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Radda [10]
3 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]3 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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Step-by-step explanation:

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2 years ago
Marshall invest $4500 into an account bearing 6% interest compounded semiannually. How much interest will be added into this acc
Sphinxa [80]

Answer:

$1547.62

Step-by-step explanation:

The principal Marshall invested is $4500.

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The compound interest formula is

A=P(1+r)^n

We substitute P=4500,r=0.06 and t=5 to obtain:

A=4500(1+ \frac{0.06}{2} )^ {2 \times 5}

We simplify to get:

A=4500(1+ 0.03)^ {10} = 4500 \times  {1.03}^{10}

This gives us:

A=6047.62

The interest after 5 years is

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4 0
3 years ago
second angle of a triangle is 10 degrees larger than the first angle. Third angle is 10 larger than second angle. Find the small
Papessa [141]

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Step-by-step explanation:

8 0
2 years ago
Please help!!!!!!! just click on picture to see question
scoundrel [369]

Answer:

g(n) = - 19 + (n - 1)*6

Step-by-step explanation:

The way to do this is to try a couple and then see if you can make some sort of equation that follows the rule.

g(1) = - 19

=============

g(2) = g(2 - 1) + 6

g(2) = g(1) + 6

g(2) = -19 + 6

g(2) = -13

=============

g(3) = g(2) + 6

g(3) = -13 + 6

g(3) = - 7

==========

g(4) = g(3) + 6

g(4) = - 7 + 6

g(4) = - 1

==========

g(5) = 5

g(6) =11

===========

Now the hard part. You have to start  with - 19

The nth term is g(n) = - 19 + (n - 1)*6

Now see if it works.

g(7) = - 19 + (7 - 1)*6

g(7) = - 19 + 6 * 6

g(7) = -19 + 36

g(7) = 17

Is that correct?

g(7) = g(n - 1) + 6

g(7) = g(6) + 6

g(7) = 11 + 6

g(7) = 17 Seems to be the same as the explicit formula gives.

3 0
3 years ago
3.225×100 is what again let see who gets it
Sonbull [250]
This would result in 322.5. you get this by moving the decimal place two to the right
6 0
3 years ago
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