Question

If A=(1,2,3) B=(4,5,6) C=(7,8,9) verify that AU(BnC)=(AUB)n(AUC)

Answer 1

Step-by-step explanation:

A = { 1,2,4,5 }

B = { 2,3,5,6 }

C = { 4,5,6,7 }

A u B = { 1,2,3,4,5,6}

A u C = {1,2,4,5,6,7 }

(A u B ) intersection (A u c) = { 1,2,4,5,6 } ---- equation 1

(B intersection C) = { 5,6 }

A u ( B intersection C) = { 1,2,4,5,6 } ------ equation 2

Hence equation 1 is equal to equation 2

A u (B intersection C) =(A u B) intersection (A u C)

Hence verified

Answer 2

If A = (1,2,3) , B = (4,5,6) and C = (7,8,9).

We have to verify that A∪(B∩C) = (A∪B) ∩ (A∪C)

Concepts :

• Union of two or more sets : It is the set containing all the elements of given sets. It is generally written by symbol 'U'. for example, p = (1.2) and q = (3,4) are two sets, then union of p and q = p ∪ q = (1,2,3,4)
• Intersection of two or more sets : It is the set containing all the common elements of given sets. It is generally written by symbol '∩'. for example, two sets p = (1,2) and q = (1,2,3,4) then intersection of p and q = p ∩ q = (1.2)

LHS = A∪(B∩C)

= (1,2,3) ∪ [(4,5,6) ∩ (7,8,9)]

= (1,2,3) ∪ Ф

= (1,2,3)

RHS = (A∪B) ∩ (A∪C)

= [(1,2,3) ∪ (4,5,6)] ∩ [(1,2,3) ∪ (7,8,9)]

= (1,2,3,4,5,6) ∩(1,2,3,7,8,9)

= (1,2,3)

It is clear that, LHS = RHS

Hence verified.

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