Answer to Question #264359 in Discrete Mathematics for Liz

Question #264359

Use properties of Boolean algebra to simplify the following Boolean expression (showing all the steps):


(y′)(x′ + y′)′



1
Expert's answer
2021-11-12T03:56:07-0500

Use properties of Boolean algebra let us simplify the following Boolean expression:


(x+y)(x+y)=(x+y)(xy)=(x+y)(xy)=xxy+yxy=xy+yyx=xy+0x=xy+0=xy(x + y')(x' + y')'= (x + y')(x'' \cdot y'')= (x + y')(x\cdot y)\\= x\cdot x\cdot y + y'\cdot x\cdot y= x\cdot y + y'\cdot y\cdot x= x\cdot y +0\cdot x\\= x\cdot y +0=x\cdot y



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