Question

Show that: 1) Au(AnB)=A
2)An(AuB)=A

Answer 1

Answer:

Both statements are true.

Step-by-step explanation:

1. A U (A ∩ B) = A ( to show)

Simplyfying LHS

A U (A ∩ B)  = (A U A)  ∩ (A U B)   (distributive law)

                                                 = A ∩ (A U B)

Also, A intersection with A U B will always be A as A is the smaller set of the two.

So, A U (A ∩ B) = A

2. A ∩ (A U B) = A

Simplyfying LHS

A ∩ (A U B)  = (A ∩ A) U (A ∩ B)   (distributive law)

                                                 = A U (A ∩ B)

Also, A union with A ∩ B will always be A as A is the bigger set of the two.

So, A ∩ (A U B) = A