Q13 of 58 Page 12

Determine whether each of the statement in

For all sets A and B, (A – B) ∪ (A ∩ B) = A

Given: There are two sets A and B


To check: (A – B) ∪ (A ∩ B) = A is true or false


Take L.H.S


(A – B) ∪ (A ∩ B)


= (A ∩ B’) ∪ (A ∩ B) {∵ A – B = A ∩ B’}


= A ∩ (B’ ∪ B)


{∵ Distributive property of set:


(A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C)}


= A ∩ U


= A


= R.H.S


Hence, the given statement is true


More from this chapter

All 58 →
11

Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S.

 12

For all sets A, B and C, show that (A – B) ∩ (A – C) = A – (B ∪ C)

 14

Determine whether each of the statement in

For all sets A, B and C, A – (B – C) = (A – B) – C

 15

Determine whether each of the statement in

For all sets A, B and C, if A ⊂ B, then A ∩ C ⊂ B ∩ C