Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find:
i) Ax(B ∩ C)
ii) (AxB) ∩ (AxC)
iii) Ax(B ∪ C)
iv) (AxB) ∪ (AxC)
Answers
Step-by-step explanation:
In this question
We have been given that
A = {1,2,3,4} , B = {4,5,6} , C = {5,6}
We need to find the following
(i) A×(B ∩ C)
(B ∩ C} = {5,6}
Therefore A×(B ∩ C) = {(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)}
(ii) (A×B) ∩ (A×C)
(A×B) = {(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,4),(4,5),(4,6)}
(A×C) = {(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)}
Therefore, (A×B) ∩ (A×C) = {(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)}
(iii) A×(B ∪ C)
(B ∪ C) = {4,5,6}
Therefore, A×(B ∪ C) = {(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),93,4),(3,5),(3,6),(4,4),(4,5),(4,6)}
(iv)(A×B) ∪ (A×C)
(A×B) = {(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,4),(4,5),(4,6)}
(A×C) = {(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)}
Therefore, (A×B) ∪ (A×C) = {(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,4),(4,5),(4,6)}