Q9 of 50 Page 14

Using Venn diagram, verify whether the following are true:

A (B ∪ C) = (A B) ∩ (A C)

A (B ⋃ C) = (A B) ⋂ (A C)


LHS:


Consider B ⋃ C,



Then, A (B ⋃ C)


= LHS


RHS:


Consider A B,



Then, consider A C,



Then, (A B) ⋂ (A C)


= RHS


∴ LHS = RHS


Hence proved.


More from this chapter

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9

Using Venn diagram, verify whether the following are true:

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

 9

Using Venn diagram, verify whether the following are true:

(A ∪ B)’ = A’ ∩ B’

 1

If A and B are two sets and U is the universal set such that n(∪) = 700, n(A) = 200, n(B) = 300 and n (A ∩ B) = 100,find n(A’ ∩ B’).

 2

Given n(A) = 285, n(B) = 195, n(∪) = 500, n(A ∪ B) = 410, find n(A’ ∩ B’).