1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lidiya [134]
3 years ago
10

Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф

Mathematics
1 answer:
asambeis [7]3 years ago
4 0

Answer:

a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

Therefore;

(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B)  = (A ∩ B) (Addition to zero identity property)

∴  A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

You might be interested in
What solid fits snugly through each shape when held in the right position -square, triangle, circle
Nana76 [90]

Answer:

Im pretty sure its circle

7 0
3 years ago
Read 2 more answers
PLZ HELPPP!!!!!!!!!! ASAP
salantis [7]

Answer:

They are consecutive terms in the Fibonacci Sequence.

Step-by-step explanation:

The sequence goes 1,1,2,3,5,8,13,21,...

Since 13 and 21 are consecutive here, that is the answer.

8 0
2 years ago
What is the first step in solving the equation 3.5 n + 6.4 = 42.5?
miss Akunina [59]

I would add like terms, meaning subtract 6.4 from both sides.

3.5n = 36.1

7 0
3 years ago
Read 2 more answers
What are the solutions to the quadratic equation (5y + 6)2 = 24?
Ivenika [448]

Answer:

y = \frac{2\sqrt{6} }{5} -\frac{6}{5}  OR  y = \frac{-2\sqrt{6} }{5} -\frac{6}{5}

Step-by-step explanation:

Our quadratic equation is: (5y + 6)² = 24.

The first step is to square root both sides:

5y + 6 = ±√24 = ±2√6

Now subtract 6 from both sides:

5y = ±2√6 - 6

Finally divide by 5 from both sides:

y = \frac{2\sqrt{6} }{5} -\frac{6}{5}  OR  y = \frac{-2\sqrt{6} }{5} -\frac{6}{5}

And, those are the solutions to the equation.

7 0
3 years ago
Read 2 more answers
What is the domain of ƒ(x) if ƒ(x) = 1 x – 4?
Alina [70]
The domain would negative infinity to positive infinity . Domain would be the smallest through the largest possibly value of X. If you also need the range it’s ( -4,infinity]
3 0
3 years ago
Other questions:
  • How to solve 8(3p-1)+9=3(p+2)-1 ?
    13·1 answer
  • A class of 64 students was given 320 book how many will each students take home
    12·1 answer
  • Find two SQUARE numbers that have a sum of 130
    5·1 answer
  • Use the points A(3,-2) and B(-1,-6) to answer the question.
    13·1 answer
  • What is it in fraction form?
    8·2 answers
  • Find the value 12 to the second power
    14·2 answers
  • Help plz i will do anything man i need to pass math
    9·2 answers
  • Can you help me please?
    8·2 answers
  • Which number is an integer? <br><br> A: -9,248.3<br> B: -16/17 <br> C: 10,839<br> D: 35,749.087
    7·1 answer
  • I need help on this question:<br> Identify the bases and faces of each figure. Then name the figure
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!