Boolean Identities

Tutorial Sheet $2$

$4$G$+$

$42\%$

:

$1.$ OR Law

$2.$ AND Law

$($a$)$ A $+0=$ A

$($b$)$ A $+1=1($c$)$

A $+$ A $=$ A$($d$)*$ A $+$ A $=1(1)$A bullet overline A $=0$

$($a$)$ A $*0=$ l

$($b$)$ A $*1=$ A

$($C$)$AAA

$3.$ Compliment Law $4.$ Commutative Law

$($a$)1=0$

$($b$)01$

$($c$)$

$($A$)=$A

$($a$)$ A$+$B$=$B$+$A

$($b$)$ AB$-$BA

$5.$ Associative Law

$($a$)$ A$+($B$+$C$)=($A$+$B$)+$C

$6.$ Distributive Law

$($a$)$ A $($B$+$C$)=$A$+$B$+$A$.$C

$7.$ Absorptive Law

$($a$)$ A$+$A$+$B$=$A

$($b$)$A $($A$+$B$)=$A

$($b$)$ A $($BC$)($AB$)$ C $($b$)$

A$+$B$+$C$=($A$+$B$)($A$+$C$)$

$($c$)$ A $($A$+$B$)=$AB $($b$)($A$+$B$)=$ A $+$ B

$9.$ DeMorgan's Theorem

$($a$)($A $+$ B$)=$ AR

Problems

$1.$ Verify each of the following through algebraic simplification. Apply no more than $1$ identity in each step