set theory



If universal set,U = {-2,-1,0,1,2,3,4,5,6,7,8,9,10}

Verify de morgan's law of complementation

To verify
(i) [A u B]' = A' n B'
(ii)[A n B]' = A' u B'
where u stands for union and n stands for
intersection of the sets.
to verify (i)
 A u B = {-2,1,2,3,4,5,6,7,8,9,10}
L.H.S.=[A u B]' = U \ [A u B]

A' = U \ A ={-1,0,1}
B' = U \ B = {-2,-1,0,2,4,6,7,10}

R.H.S. = A' n B' = {-1,0}--------(2)

from (1) and (2)
L.H.S. = R.H.S.

to verify (ii)
A n B = {3,5,8,9}
L.H.S=[A n B]' = U \ {A n B}

A' = U \ A ={-1,0,1}
B' = U \ B = {-2,-1,0,2,4,6,7,10}

R.H.S =A' u B'
       = {-2,-1,0,1,2,4,6,7,10}

L.H.S = R.H.S
Hence (ii) is verified.

problem 2

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