Let ( A = {1, 2, 3, 4, 5} ) and ( B = {4, 5, 6, 7, 8} ). Find ( A' cap B ) and ( B' cap A ), where ( A' ) and ( B' ) are the complements of sets A and B respectively in the universal set ( U = {1, 2, 3, 4, 5, 6, 7, 8} ).

Question

Let ( A = {1, 2, 3, 4, 5} ) and ( B = {4, 5, 6, 7, 8} ). Find ( A&#x27; cap B ) and ( B&#x27; cap A ), where ( A&#x27; ) and ( B&#x27; ) are the complements of sets A and B respectively in the universal set ( U = {1, 2, 3, 4, 5, 6, 7, 8} ).

Accepted Answer

Step:1 ：First, we find the complements of sets A and B. ( A&#x27; = U - A = {6, 7, 8} ) and ( B&#x27; = U - B = {1, 2, 3} ).Step:2 ：Next, we find the intersection of ( A&#x27; ) and ( B ). ( A&#x27; cap B = {6, 7, 8} cap {4, 5, 6, 7, 8} = {6, 7, 8} ).Step:3 ：Finally, we find the intersection of ( B&#x27; ) and ( A ). ( B&#x27; cap A = {1, 2, 3} cap {1, 2, 3, 4, 5} = {1, 2, 3} ).

Answer

Step: 1 ：First, we find the complements of sets A and B. ( A&#x27; = U - A = {6, 7, 8} ) and ( B&#x27; = U - B = {1, 2, 3} ).Step: 2 ：Next, we find the intersection of ( A&#x27; ) and ( B ). ( A&#x27; cap B = {6, 7, 8} cap {4, 5, 6, 7, 8} = {6, 7, 8} ).Step: 3 ：Finally, we find the intersection of ( B&#x27; ) and ( A ). ( B&#x27; cap A = {1, 2, 3} cap {1, 2, 3, 4, 5} = {1, 2, 3} ).

Let $A = {1, 2, 3, 4, 5}$ and $B = {4, 5, 6, 7, 8}$ . Find $A^{'} \cap B$ and $B^{'} \cap A$ , where $A^{'}$ and $B^{'}$ are the complements of sets A and B respectively in the universal set $U = {1, 2, 3, 4, 5, 6, 7, 8}$ .

Answer

Popular Problems

Let A={1,2,3,4,5} and B={4,5,6,7,8}. Find A′∩B and B′∩A, where A′ and B′ are the complements of sets A and B respectively in the universal set U={1,2,3,4,5,6,7,8}.

Answer

Popular Problems

Let $A = {1, 2, 3, 4, 5}$ and $B = {4, 5, 6, 7, 8}$ . Find $A^{'} \cap B$ and $B^{'} \cap A$ , where $A^{'}$ and $B^{'}$ are the complements of sets A and B respectively in the universal set $U = {1, 2, 3, 4, 5, 6, 7, 8}$ .