Question

please answer this question

Answer 1

Answer:

your answer is in above pic

Step-by-step explanation:

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Answer 2

Given :-

• U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
• A = {1, 3, 5, 7, 8}
• B = { 1, 2, 3, 4}
• C = {3, 4, 6, 8}

To verify :-

• A- (B ∩ C) = (A- B ) ∪ (A- C)
• (A ∪B)' = A' ∩ B '

Solution :-

Firstly take 1st Question

A- (B ∩ C) = (A- B ) ∪ (A- C)

Take L.H.S

A- (B ∩ C )

We find first (B ∩ C )

(B ∩ C ) = { 1, 2, 3, 4} ∩ { 3, 4, 6, 8}

(B ∩ C ) = { 3, 4}

So,

A- (B ∩ C ) = {1, 3, 5, 7 , 8} - {3,4}

A- (B ∩ C ) = { 1, 5, 7, 8}

L.H.S = {1, 5, 7, 8}

Now take R.H.S

(A- B ) ∪ (A- C)

Firstly we find A- B and A-C

A- B = {1, 3, 5, 7, 8} - {1, 2, 3, 4}

A-B = { 5, 7, 8}

A- C = {1, 3, 5, 7, 8} - { 3, 4, 6, 8}

A- C = { 1, 5 , 7, 8}

Now , finding

(A- B ) ∪ (A- C)

{ 5, 7, 8} ∪ { 1, 5, 7, 8}

{1, 5, 7, 8}

(A- B ) ∪ (A- C) = {1, 5, 7, 8}

R.H. S = {1, 5, 7, 8}

L.H.S = R.H.S = {1, 5 ,7, 8}

Hence verified!

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Now solving the 2nd Question,

(A ∪B)' = A' ∩ B '

Take L.H.S

(A ∪ B)'

Firstly we find the ( A∪B)

( A∪B) = {1, 3, 5, 7, 8} ∪ {1, 2, 3, 4}

( A∪B) = {1, 2, 3, 4, 5, 7,8}

We know that,

(A ∪ B)' = U - ( A∪B)

So,

(A ∪ B)' = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} - {1, 2, 3, 4, 5, 7,8}

(A ∪ B)' = { 6, 9 , 10}

L.H.S = { 6, 9 , 10}

Now take R.H.S

A' ∩ B '

Firstly we find A' , B'

A' = U - A

B' = U - B

A' = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} - {1, 3, 5, 7, 8}

A' = { 2, 3, 4 ,6 , 9, 10}

B' = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} - { 1, 2, 3, 4}

B' = { 5, 6, 7, 8, 9, 10}

A' ∩ B ' = { 2, 3, 4 ,6 , 9, 10} ∩ { 5, 6, 7, 8, 9, 10}

A' ∩ B ' = {6, 9, 10}

R.H.S = {6, 9, 10}

So, L.H.S = R.H.S = {6, 9, 10}

Hence Verified !

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