ODA a "ll ZAIN IQZ Lec5 Bool...14Digital SystemsMustafa Al-HashimiEX| Prove the relation is true :x y + xy = x y + x ySOL\Right hand side (RHS):-x y +xy = x y.xyDeMorgan's Theorem= == (x +y) (x+y)Rule 9: x = x= (x+y) (x+y)Factoring (distributive law)= xx + xy + y x + yyRule 8: xx = 0, y y= 0= x y + y xTherefore the relation is trueLeſt hand side (LHS):-x y + xy = xy. x yFactoring (distributive law)DeMorgan's Theorem= (x + y) (x + y)Rule 9: x = x= (x+y) (x + y)Factoring (distributive law)= xx + x y + y x + yyRule 8: xx = 0, y y= 0= x y + y xTherefore the relation is trueHW1- Implement (R = A O B) by using only NAND gates that two input, applyDeMorgan's theorems15

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1- Implement (R = A O B) by using only NAND gates that two input, apply DeMorgan's theorems

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Question

ODA a "ll ZAIN IQ
Z Lec5 Bool...
14
Digital Systems
Mustafa Al-Hashimi
EX| Prove the relation is true :
x y + xy = x y + x y
SOL\
Right hand side (RHS):-
x y +xy = x y.xy
DeMorgan's Theorem
= =
= (x +y) (x+y)
Rule 9: x = x
= (x+y) (x+y)
Factoring (distributive law)
= xx + xy + y x + yy
Rule 8: xx = 0, y y= 0
= x y + y x
Therefore the relation is true
Leſt hand side (LHS):-
x y + xy = xy. x y
Factoring (distributive law)
DeMorgan's Theorem
= (x + y) (x + y)
Rule 9: x = x
= (x+y) (x + y)
Factoring (distributive law)
= xx + x y + y x + yy
Rule 8: xx = 0, y y= 0
= x y + y x
Therefore the relation is true
HW
1- Implement (R = A O B) by using only NAND gates that two input, apply
DeMorgan's theorems
15

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