Question

Let A,B and C be sets then show that:-
A intersection(B union C)= (A intersection B) union( A intersection C)

Answer 1

Step-by-step explanation:

• From (1) and (2)
• From (1) and (2) A ∩ (B U C) =(A ∩ B)U(A ∩ C)

Answer 2

Answer:

The correct answer to this question is,

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) is verified.

Step-by-step explanation:

Union:

The union of a set consists of all the elements present in the Sets

Intersection:

The intersection of a set consists of the elements which are only common in the sets

Let us take an example and we will verify this question by this example.

A = { 1, 2, 3, 4, 8, 10 }

B = { 2, 3, 5, 7, 9, 10 }

C = { 1, 2, 3, 4, 5, 6 }

Now, L.H.S = A ∩ (B ∪ C)

(B ∪ C) = { 2, 3, 5, 7, 9, 10 } ∪ { 1, 2, 3, 4, 5, 6 }

(B ∪ C) =  { 1, 2, 3, 4, 5, 6, 7, 9, 10 }

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

A ∩ (B ∪ C) = { 1, 2, 3, 4, 10 }

Now, R.H.S = (A ∩ B) ∪ (A ∩ C)

(A ∩ B) =  { 1, 2, 3, 4, 8, 10 } ∩ { 2, 3, 5, 7, 9, 10 }

(A ∩ B) =  { 2, 3, 10 }

(A ∩ C) = { 1, 2, 3, 4, 8, 10 } ∩ { 1, 2, 3, 4, 5, 6 }

(A ∩ C) = { 1, 2, 3, 4 }

(A ∩ B) ∪ (A ∩ C) = { 2, 3, 10 } ∪ { 1, 2, 3, 4 }

(A ∩ B) ∪ (A ∩ C) = { 1, 2, 3, 4, 10}

We can see, L.H.S  = R.H.S

∴ A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Hence we show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)  (verified)

Click here for more about the union set:

https://brainly.in/question/7566103

Click here for more about the intersection set:

https://brainly.in/question/29801008