Q. 6 A3.5( 4 Votes )

Let U = {1, 2, 3,

Answer :

A B = {x: x ϵ A or x ϵ B}


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


(AB)’ means Complement of (AB) with respect to universal set U.


So, (AB)’ = U – (AB)’


U – ( AB)’ is defined as {x ϵ U : x (AB)’}


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


(AB)’ = {2, 3, 4, 5, 6, 7, 8}


U – ( AB)’ = {1, 9}


Now


A’ means Complement of A with respect to universal set U.


So, A’ = U – A


U – A is defined as {x ϵ U : x A}


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


A = {2, 4, 6, 8}


A’ = {1, 3, 5, 7, 9}


B’ means Complement of B with respect to universal set U.


So, B’ = U – B


U – B is defined as {x ϵ U : x B}


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


B = {2, 3, 5, 7}.


B’ = {1, 4, 6, 8, 9}


A’ B’ = = {x:x ϵ A’ and x ϵ C’}.


= {1, 9}


Hence verified.


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