Question

Mishradibyanshnu if u={1,2,3,4,5,6,7,8,9}A=2,4,6,8,} and B{2,3,5,7,} verify that (AUB)=AnB

Answer 1

Step-by-step explanation:

If U={1,2,3,4,5,6,7,8,9},A={2,4,6,8} and B={2,3,5,7}, verify that:

(A∩B)

′

=(A

′

∪B

′

)

Medium

Solution

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Given U={1,2,3,4,5,6,7,8,9}

A={2,4,6,8}, B={2,3,5,7}

1) A∩B={2,4,6,8}∩{2,3,5,7}

∴A∩B={2}

∴(A∩B)

′

={1,3,4,5,6,7,8,9} Equation (1)

2) A

′

={1,3,5,7,9}

B

′

={1,4,6,8,9}

A

′

∪B

′

={1,3,5,7,9}∪{1,4,6,8,9}

∴A

′

∪B

′

={1,3,4,5,6,7,8,9} Equation (2)

From equation (1) and (2),

(A∩B)

′

=A

′

∪B

′