Question

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)

Answer 1

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Answer 2

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)}