Higher Engineering Mathematics

100 NUMBER AND ALGEBRA

Problem 7. Simplify

F·G·H+F·G·H+F·G·H

With reference to Table 11.8: Reference

F·G·H+F·G·H+F·G·H

=F·G·(H+H)+F·G·H 5

=F·G· 1 +F·G·H 10

=F·G+F·G·H 12

=G·(F+F·H)5

Problem 8. Simplify

F·G·H+F·G·H+F·G·H+F·G·H

With reference to Table 11.8: Reference

F·G·H+F·G·H+F·G·H+F·G·H

=G·H·(F+F)+G·H·(F+F)5

=G·H· 1 +G·H· 110

=G·H+G·H 12

=H·(G+G)5

=H· 1 =H 10 and 12

Problem 9. Simplify

A·C+A·(B+C)+A·B·(C+B)

using the rules of Boolean algebra.

With reference to Table 11.8: Reference

A·C+A·(B+C)+A·B·(C+B)

=A·C+A·B+A·C+A·B·C

+A·B·B 5

=A·C+A·B+A·C+A·B·C

+A· 014

=A·C+A·B+A·C+A·B·C 11

=A·(C+B·C)+A·B+A·C 5

=A·(C+B)+A·B+A·C 17

=A·C+A·B+A·B+A·C 5

=A·C+B·(A+A)+A·C 5

=A·C+B· 1 +A·C 10

=A·C+B+A·C 12

Problem 10. Simplify the expression

P·Q·R+P·Q·(P+R)+Q·R·(Q+P),

using the rules of Boolean algebra.

With reference to Table 11.8: Reference

P·Q·R+P·Q·(P+R)+Q·R·(Q+P)

=P·Q·R+P·Q·P+P·Q·R

+Q·R·Q+Q·R·P 5

=P·Q·R+ 0 ·Q+P·Q·R+ 0 ·R

+P·Q·R 14

=P·Q·R+P·Q·R+P·Q·R 7 and 11

=P·Q·R+P·Q·R 9

=P·R·(Q+Q)5

=P·R· 110

=P·R 12

Now try the following exercise.

Exercise 47 Further problems on the laws

and the rules of Boolean algebra

Use the laws and rules of Boolean algebra

given in Table 11.8 to simplify the following

expressions:

1.P·Q+P·Q [P]

2.P·Q+P·Q+P·Q [P+P·Q]

3.F·G+F·G+G·(F+F)[G]

4.F·G+F·(G+G)+F·G [F]

5. (P+P·Q)·(Q+Q·P)[P·Q]

6.F·G·H+F·G·H+F·G·H

[H·(F+FG]

7.F·G·H+F·G·H+F·G·H

[F·G·H+G·H]

8.P·Q·R+P·Q·R+P·Q·R

[Q·R+P·Q·R]

9.F·G·H+F·G·H+F·G·H+F·G·H

[G]

10.F·G·H+F·G·H+F·G·H+F·G·H

[F·H+G·H]

11.R·(P·Q+P·Q)+R·(P·Q+P·Q)

[P·R+P·R]

12.R·(P·Q+P·Q+P·Q)+P·(Q·R+Q·R)

[P+Q·R]