Page 33 - CITS - Electronic Mechanic - TT - 2024

ELECTRONICS MECHANIC - CITS

A’C+ BC =

AB + A’C Proof: L.H.S.=AB+ A’C +BC
=AB +A’C+ BC(A+A’)
=AB +A’C+ BCA+BCA’
=AB(1 +C)+ A’C(1 +B)
=AB +A’C

=R.H.S.
This theorem can be extended as,
AB+A’C+BCD= AB+A’C
Theorem 2:(A+ B)(A’+C)(B+ C) =(A+ B)(A’+C)
Proof : L.H.S.=(A+B)(A’+ C)(B +C)

=(AA’+AC+A’B+BC) (B+C)
=(0+ AC+A’B+ BC)(B +C)
=ACB +ACC+A’BB +A’BC+BCB +BCC
=ABC+AC+ A’B+A’BC+ BC+BC

=ABC+AC+A’B+A’BC+BC
=AC(1 + B)+A’B(1+ C) +BC
= AC+ A’B+BC (1)
R.H.S.=(A+B)(A’+C)
= AA’+AC+ BA’+BC
=0 +AC+BA’+BC

= AC+ A’B+BC (2)
Equation (1) = Equation (2)So.
L.H.S = R.H.S.
This theorem can be extended to any no.of variables.

(A+ B)(A’+C) (B +C+ D)=(A+B)(A’+C)
Transposition theorem:
Theorem:
AB +A’C=
(A+ C)(A’+B) Proof: R.H.S.=(A+C)(A’+B)

=AA’+ AB+CA’+CB
=0+AB+CA’+CB
=AB+CA’+CB
=AB+A’C (B’cz of AB+A’C+BC= AB+A’C)

=L.H.S.
DeMorgan’sTheorem:
Law1: (A+ B)’=A’· B’
Proof:
Law2: (A· B)’=A’+B’

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CITS : E & H - Electronics Mechanic - Lesson 5 - 8