Q3 of 145 Page 33

If A = {x : x ϵ N, x ≤ 7}, B = {x : x is prime, x < 8} and C = {x : x ϵ N, x is odd and x < 10}, verify that:

(i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)


(ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)


Natural numbers start from 1


A = {1, 2, 3, 4, 5, 6, 7}


B = {2, 3, 5, 7}


C = {1, 3, 5, 7, 9}


(i) BC = {3, 5, 7}
AU(BC) = {1, 2, 3, 4, 5, 6, 7}


AB = {1, 2, 3, 4, 5, 6, 7}


AC = {1, 2, 3, 4, 5, 6, 7, 9}


(AB)(AC) = {1, 23, 4, 5, 6, 7}


A(BC) = (AB)(AC)


Hence proved


(ii) BC = {1, 2, 3, 5, 7, 9}


A(BC) = {1, 2, 3, 5, 7}


AB = {2, 3, 5, 7}


AC = {1, 3, 5, 7}


(AB)(AC) = {1, 2, 3, 5, 7}


A(BC) = (AB)(AC)


Hence proved


More from this chapter

All 145 →
1

If A = {a, b, c, d, e}, B = {a, c, e, g}, verify that:

(i) A ∪ B = B ∪A


(ii) A ∪ C = C ∪ A


(iii) B ∪ C = C ∪ B


(iv) A ∩ B = B ∩ A


(v) B ∩ C = C ∩ B


(vi) A ∩ C = C ∩ A


(vii) (A ∪ B ∪ C = A ∪ (B ∪ C)


(viii) (A ∩ B) ∩ C = A ∩ (B ∩ C)


 2

If A = {a, b, c, d, e}, B = {a, c, e, g}, and C = {b, e, f, g} verify that:

(i) A ∩ (B – C) = (A ∩ B) – (A ∩ C)


(ii) A – (B ∩ C) = (A – B) ∪ (A – C)


 4

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}, and = {2, 3, 5, 7} verify that:

(i) (A ∪ B)’ = (A’ ∩ B’)


(ii) (A ∩ C)’ = (A’ ∪ B’)


 5

Let A = {a, b, c}, B = {b, c, d, e} and = {c, d, e, f} be subsets of U = {a, b, c, d, e, f}. Then verify that:

(i) (A’)’ = A


(ii) (A ∪ B)’ = (A’ ∩ B’)


(iii) (A ∩ B)’ = (A’ ∪ B’)