Page 29 - Computer_Science_F5

Computer Science Step 1: Determine the terms you can apply DeMorgan’s theorem and treat each
Solution:

term as a single variable.

will be:
Step 2: Using DeMorgan’s theorem, the expression ABC BC+
FOR ONLINE READING ONLY
ABC
. BC
ABC BC
    
   
Step 3: Using DeMorgan’s theorem, the expression ABC . BC will be:
. BC
ABC BC   A BC   

Step 4: Using laws of Algebra

ABC BC   A BC   
. BC

. BC
ABC BC   A BC    - Double negation

ABC BC+ = AB AC BB BC BC CC+ + + + + - Distributive law

ABCBC+ = AB ACBCBC CC+ + + + - Complementary law
ABCBC+ = AB ACBCBC C+ + + + - Idempotent law

ABC BC+ = AB AC BC C+ + + (B + 1) - Distributive law

ABC BC+ = AB AC BC C+ + + .1 - Annulment law
ABC BC+ = AB AC BC C+ + + - Identity law

ABC BC+ = AB C+ (A B+ + 1) - Distributive law
1 1
ABC BC AB C+ = + (A+ 1) - Annulment law, B +=
1 1
ABC BC AB C+ = + .1 - Annulment law, A+=
ABC BC+ = AB C+ - Identity law

Exercise 1.4 (d) ABC + AC + ABC
1. Use DeMorgan’s theorem and laws 2. Use the truth table to prove the
of Boolean algebra to simplify the following DeMorgan’s theorem:
following expressions:
. AB = A B+
(a) ABC + ABC 3. Demonstrate DeMorgan’s theorem
(b) BC BC+ + AC using a truth table for the expression:
(c) B AB ABC+ + ABC = A+ B + C

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for Advanced Secondary Schools

Computer Science Form 5.indd 20 23/07/2024 12:32