Q. 44.0( 53 Votes )

If U = {1,

Answer :

(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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