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

Review exercises 5 197
12 (a) A·B+A·B+A·B
(b) A·B +A·B
(c) A ·B·C +A ·B·C+A·B·C+A·B·C
(d) A·B·C+A·B·C+A·B·C
13 (A ·B)·(A·B)
REVIEWEXERCISES5
1 Classifythe followingastrue orfalse:
(a) R + ⊂ R
(c) 0.667∈Q
(e) −6∈Q
(g) N∩Q=N
(b) 0.667 ∈ R −
(d) N∪Z=R
(f)9/∈ R
(h) R − ∩Q=◦/
2 Useset notationto describethe followingintervals on
thexaxis.
(a) [−6,9] (b) (−1,1) (c) |x| < 1.7
(d) (0,2] (e) |x| > 1 (f) |x| 2
3 ThesetsA,BandC are given by
A = {1,2,6,7,10,11,12,13},B = {3,4,7,8,11},
C = {4,5,6,7,9,13} andthe universal set
E = {x :x∈N + ,1 x13}.Listthe elements of
the following sets:
(a) A∪B (b)B∪C (c)A∩B
(d) A∩(B∪C) (e)A∩B∩C
(f) A∪(B∩C) (g)C∪(B∩A)
4 Representthe setsA,BandC describedin Question3
onaVenn diagram.
5 List allthe elementsofthe followingsets:
(a) S={n:n∈Z,5n 2 50}
(b) S={m:m∈N,5m 2 50}
(c) S={m:m∈N,m 2 +2m−15=0}
6 IfA={n:n∈Z,−10n20},
B={m:m∈N,m>15}listthemembersofA∩B
andwrite down an expression forA ∪B.
7 WriteBooleanexpressions forthe output,F,from the
electronic devices shown in Figure5.23.
8 Simplify the followingBoolean expressions usingthe
laws ofBooleanalgebra:
(a) A·B·1
(c) 1+0
(e) (A+C)·(C+A)
(f) A·B+A +B (g) A·B
(h) A +B
(b) A+A·B+B
(d) D·(C+B)+C·D
(i) A·(B+C)·C
(j) (C+A+D)·(C·D+A)
9 Draw uptruthtables to verifythatA·B +B and
A ·B +A are logically equivalent.
A
B
F
(a)
C
A
B
F
(b)
(c)
A
B
C
D
Figure5.23
F