Let ( A = {1, 2, 3, 4, 5} ) and ( B = {3, 4, 5, 6, 7} ) be two sets in the universal set ( U = {1, 2, 3, 4, 5, 6, 7} ). Find the complement of the set ( A bigcup B ) in ( U ).

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Accepted Answer

Step:1 ：Step 1: Find the union of sets ( A ) and ( B ), denoted as ( A bigcup B ). The union of two sets is the set of elements which are in ( A ), in ( B ), or in both ( A ) and ( B ). So, ( A bigcup B = {1, 2, 3, 4, 5, 6, 7} ).Step:2 ：Step 2: The complement of a set ( A ) in a universal set ( U ), denoted by ( A&#x27; ) or ( overline{A} ), is the set of elements in ( U ) but not in ( A ). Therefore, the complement of ( A bigcup B ) in ( U ) is ( U - (A bigcup B) ).Step:3 ：Step 3: Subtracting the elements of ( A bigcup B ) from the universal set ( U ), we get ( U - (A bigcup B) = emptyset ), which is the empty set because all elements of ( A bigcup B ) are in the universal set ( U ).

Answer

Step: 1 ：Step 1: Find the union of sets ( A ) and ( B ), denoted as ( A bigcup B ). The union of two sets is the set of elements which are in ( A ), in ( B ), or in both ( A ) and ( B ). So, ( A bigcup B = {1, 2, 3, 4, 5, 6, 7} ).Step: 2 ：Step 2: The complement of a set ( A ) in a universal set ( U ), denoted by ( A&#x27; ) or ( overline{A} ), is the set of elements in ( U ) but not in ( A ). Therefore, the complement of ( A bigcup B ) in ( U ) is ( U - (A bigcup B) ).Step: 3 ：Step 3: Subtracting the elements of ( A bigcup B ) from the universal set ( U ), we get ( U - (A bigcup B) = emptyset ), which is the empty set because all elements of ( A bigcup B ) are in the universal set ( U ).

Let $A = {1, 2, 3, 4, 5}$ and $B = {3, 4, 5, 6, 7}$ be two sets in the universal set $U = {1, 2, 3, 4, 5, 6, 7}$ . Find the complement of the set $A ⋃ B$ in $U$ .

Answer

Popular Problems

Let A={1,2,3,4,5} and B={3,4,5,6,7} be two sets in the universal set U={1,2,3,4,5,6,7}. Find the complement of the set A⋃B in U.

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Popular Problems

Let $A = {1, 2, 3, 4, 5}$ and $B = {3, 4, 5, 6, 7}$ be two sets in the universal set $U = {1, 2, 3, 4, 5, 6, 7}$ . Find the complement of the set $A ⋃ B$ in $U$ .