Page 170 - FUNDAMENTALS OF COMPUTER

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170 Fundamentals of Computers NPP

9. A + B = B + A
Proof: Consider the following table: {ZåZ Vm{bH$m ~ZmAmo…

A B A+B B+A
0 0 0 0
0 1 1 1
1 0 1 1
1 1 1 1

The values of expression A + B and B + A AV … A + B d B + A ~am~a h¡Ÿ& Š`m|{H$ BZ XmoZm|
are same for all combinations of A and B. ì`§OH$m| Ho$ _mZ ha ~ma g_mZ Am aho h¢Ÿ&
10. A.B = B.A
Proof: Consider the following table: Proof: {ZåZ Vm{bH$m H$mo ~ZmAmo …

A B A.B B.A
0 0 0 0

0 1 0 0
1 0 0 0
1 1 1 1

The expressions A.B and B.A are similar AV… A d B Ho$ g^r _mZm| Ho$ {bE A.B VWm B.A
for all values of A and B. ~am~a h¡Ÿ&
11. A + (B + C) = (A + B) + C
Proof: Consider the following Table: Proof: {ZåZ Vm{bH$m H$mo ~ZmAmo …
A B C A + (B + C) (A + B) + C
0 0 0 0 0
0 0 1 1 1
0 1 0 1 1
0 1 1 1 1
1 0 0 1 1

1 0 1 1 1
1 1 0 1 1
1 1 1 1 1

Thus, the expression in forth column is Bg àH$ma, Mm¡Wo H$m°b_ H$m g_rH$aU nm±Mdo H$m°b_ Ho$
equal to the expression in fifth column.
Therefore: A + (B + C) = (A + B) + C g_rH$aU Ho$ ~am~a h¡Ÿ& AV… A + (B + C) = (A + B) + C