Question

Given A= {1, 2, }, B= {3,4,5 } and C= {3, 5, 6, 7,8}, show that
(i) AU B=BUA
(ii) (ANB) nC= An (B nC)​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

Given:

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

To Show:

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

Solution:

Here we have to show that,

A ∪ B = B ∪ A

Taking the LHS of the equation

A ∪ B = {1,2} ∪ {3, 4, 5}

That is,

A ∪ B = {1, 2, 3, 4, 5} ------(1)

Now taking the RHS of the equation,

B ∪ A ={3, 4, 5} ∪ {1, 2}

That is,

B ∪ A = {3, 4, 5, 1, 2}-----(2)

From equations 1 and 2, the RHS are equal, hence LHS must also be equal.

∴ A ∪ B = B ∪ A

Now we have to prove that (A ∩ B) ∩ C = A ∩ (B ∩ C)

Taking the LHS of the equation,

(A ∩ B) ∩ C = ( {1,2} ∩ {3,4,5}) ∩ C

(A ∩ B) ∩ C = ∅ ∩ {3, 5, 6, 7, 8}

(A ∩ B) ∩ C = ∅------(3)

Taking the RHS of the equation,

A ∩ (B ∩ C) = A ∩ ({3,4,5} ∩ {3,5,6,7,8}

A ∩ (B ∩ C) = {1,2} ∩ {3,5}

A ∩ (B ∩ C) = ∅ -----(4)

From equations 3 and 4, RHS are equal, hence LHS must also be equal.

∴ (A ∩ B) ∩ C = A ∩ (B ∩ C)

Hence proved.