Question

If A = {1,2,3,4), B = {3,4,5,6), C = {4, 5, 6, 7, 8) and universal setX = {1,2,3,4,5,6,7,8,9,10), then verify the following:i) AU(BC) = (AUB)O(AUC)ii) An(BUC)=(ANB)U(ANC)​

Answer 1

Step-by-step explanation:

X ={1,2,3,4,5,6,7,8,9,10},A={1,2,3,4},B={2,4,6,8},C={3,4,5,6}

now from the given data

A∪B={1,2,3,4,6,8},B∪C={2,3,4,5,6,8}

Now A∪(B∪C)={1,2,3,4,5,6,8}and(A∪B)∪C={1,2,3,4,5,6,8}

∴A∪(B∪C)=(A∪B)∪C={1,2,3,4,5,6,8}

A∩B={2,4},A∩C={3,4},B∪C={2,3,4,5,6,8}

Now A∩(B∪C)={2,3,4}and(A∩B)∪(A∩C)={2,3,4}

∴A∩(B∪C)=(A∩B)∪(A∩C)={2,3,4}

A

′

={5,6,7,8,9,10}

therefore (A

′

)

′

={1,2,3,4}=A