082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

198 Chapter 5 Discrete mathematics
10 ExpressA +B+C +Dusingthe Boolean
connectives AND ( · )and negation.
11 Simplify the followingexpressions usingthe laws of
Boolean algebra:
(a) (A +A)·(B+B)
(b) A·B·A
(c) (A+B)·(A+B) (d) A ·A
(e) A·B·C·D·1·0
(g) B·C·1
(f) A·B·C·B
12 Reducethe following expressions usingBoolean
algebra:
(a) A+C+A·B·(B+C)
(b) (A+B)·B·C+(A+C)·(B+A·C)
(c) (A +B)·(A +C)
13 Thetruthtables ofthe Boolean expression,X,are
given in the followingtables. Writethe disjunctive
normal formofX in eachcase.
(a)
A B X
0 0 0
0 1 1
1 0 0
1 1 0
(b)
(c)
(d)
A B X
0 0 0
0 1 0
1 0 1
1 1 0
A B C X
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1
A B C X
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 0
Solutions
1 (a)T (b)F (c)T (d)F
(e) T (f) F (g) T (h) F
2 (a) {x:x∈R,−6x9}
(b) {x:x∈R,−1<x<1}
(c) {x:x∈R,−1.7<x<1.7}
(d) {x:x∈R,0<x2}
(e) {x:x∈R,x>1orx<−1}
(f) {x:x∈R,x2orx−2}
3 (a) {1,2,3,4,6,7,8,10,11,12,13}
(b) {3,4,5,6,7,8,9,11,13}
(c) {7,11}
(d) {6,7,11,13}
(e) {7}
(f) {1,2,4,6,7,10,11,12,13}
(g) {4,5,6,7,9,11,13}
4 SeeFigureS.15.
A
1
2
11 3
10
12 6 7 13 4
FigureS.15
9
5
5 (a) S = {−7, −6, −5, −4, −3,3,4,5,6,7}
(b) S = {3,4,5,6,7}
(c) S = {3}
6 A ∩B = {16,17,18,19,20}
A∪B={m:m∈Z,m−10}
C
8
B