Simplify the following :

3. !(A*B)*(!A+B) = !A

Try it before looking at answers

3. !(A*B)*(!A+B) = !A

!(A*B)*(!A+B) = !A
  deMorgan
(!A+!B)*(!A+B)
  Distribution
!A*!A+!A*B+!A*!B+!B*B
  Inverse
!A*!A+!A*B+!A*!B+0
  Identity
!A*!A+!A*B+!A*!B
  Distribution
!A*(!A+B+!B)
  Inverse
!A*(!A+1)
  Null
!A*(1)
  Indentity
!A
AB!(A*B)*(!A+B)!A
00!(0*0)*(!0+0)
!(0)*(1+0)
1*(1)
1		!0
1
01!(0*1)*(!0+1)
!(0)*(1+1)
1*(1)
1		!0
1
10!(1*0)*(!1+0)
!(0)*(0+0)
1*(0)
0		!1
0
11!(1*1)*(!1+1)
!(1)*(0+1)
0*(1)
0		!1
0