Set#7

If U = { 1 , 2 , 3 , 4 , 5 , 6 } , A = { 2 , 4 } U=\{1,2,3,4,5,6\},A=\{2,4\} and B = { 3 , 4 , 5 } B=\{3,4,5\} then what is ( A B ) ? (A \cup B)' ?

{ 1 , 2 , 3 , 5 , 6 } \{1,2,3,5,6\} { 1 , 2 , 3 , 4 , 5 , 6 } \{1,2,3,4,5,6\} { 1 , 6 } \{1,6\} { 2 , 3 , 4 } \{2,3,4\} { 3 , 4 } \{3,4\}

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1 solution

Munem Shahriar
Aug 24, 2017

Given that,

  • U = { 1 , 2 , 3 , 4 , 5 , 6 } U=\{1,2,3,4,5,6\}

  • A = { 2 , 4 } A=\{2,4\}

  • B = { 3 , 4 , 5 } B=\{3,4,5\}

( A B ) (A \cup B)'

= U ( A B ) = U - (A \cup B)

= { 1 , 2 , 3 , 4 , 5 , 6 } { 2 , 4 } { 3 , 4 , 5 } = \{1,2,3,4,5,6\} - \{2,4\} \cup \{3,4,5\}

= { 1 , 2 , 3 , 4 , 5 , 6 } { 2 , 3 , 4 , 5 } = \{1,2,3,4,5,6\} - \{2,3,4,5\}

= { 1 , 6 } = \boxed{\{1,6\}}

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