Question

let U={1,2,3,4,5,6}, A={2,3} and B={3,4,5} Verify that (A union B)' = A' intersect B'
.​

Answer 1

Given :

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

A = {2,3}

B = {3,4,5}

To Prove :

(A U B)' = $A'\cap B'$

Proof:

A U B = {2,3,4,5}

so,

(A U B)' = {1,6} ______(i)

& now ,

A' = {1,4,5,6}

B' = {1,2,6}

so,

A' $\cap$ B' = {1,6} ___(ii)

Since, eq(i) = eq(ii) , hence proved

Answer 2

Answer:

Given :

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

A = {2,3}

B = {3,4,5}

To Prove :

(A U B)' = A'\cap B'A

′

∩B

′

Proof:

A U B = {2,3,4,5}

so,

(A U B)' = {1,6} ______(i)

& now ,

A' = {1,4,5,6}

B' = {1,2,6}

so,

A' \cap∩ B' = {1,6} ___(ii)

Since, eq(i) = eq(ii) , hence proved