# If U = {1,

(i) First solving for left hand side,

(A B)’ = U - (A B)

First we find (A B),

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

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

Now,

(A B)’ = U - (A B)

(A B)’ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 4, 5, 6, 7, 8}

(A B)’ = {1, 9}

Now, solving for right hand side,

A’ = U - A

A’ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}

A’ = {1, 3, 5, 7, 9}

B’ = U - B

B’ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7}

B’ = {1, 4, 6, 8, 9}

A’ B’ = {1, 3, 5, 7, 9} {1, 4, 6, 8, 9}

A’ B’ = {1, 9}

LHS = RHS, Hence verified.

(ii) First solving for left hand side,

(A B)’ = U - (A B)

First we find (A B),

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

(A B) = {2}

Now,

(A B)’ = U - (A B)

(A B)’ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2}

(A B)’ = {1, 3, 4, 5, 6, 7, 8, 9}

Now, solving for right hand side,

A’ = U - A

A’ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}

A’ = {1, 3, 5, 7, 9}

B’ = U - B

B’ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7}

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}

LHS = RHS, Hence verified.

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