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.


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Let A = {10, 15, 20, 25, 30, 35, 40, 45, 50}, B = {1, 5, 10, 15, 20, 30} and C = {7, 8, 15, 20, 35, 45, 48}. Verify A (B ⋂ C) = (A B) ⋃ (A C).

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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’

 9

Using Venn diagram, verify whether the following are true:

A (B ∪ C) = (A B) ∩ (A C)