Rewrite the following expression without parenthesis and in

Re-write the following expression without parenthesis, and in a form such that each of the variables appears only once.

(a\'+b)\'+(ab\')\'cd\'

Hint:
The neccessary reduction may become more apparent after applying DeMorgans\' theorem to part of the expression.

Solution

after removing parenthesis => a\'+b\'+ab\'\'cd\' =a\'+b\'+abcd\'

a\'+b\'=(ab)\' => (ab)\'+abcd\'

=> (((ab)\'+abcd\')\')\'

=> ((ab)\'\'.(abcd\')\')\'

=> ((ab). (abcd\')\')\'

=> ((ab).((ab)\'+(cd\')\')\'

=> ((ab).(ab)\' +ab(cd\')\')\'           [A.A\'=0]

=> (ab(cd\')\')\'