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

182 Chapter 5 Discrete mathematics
(c) {x:x∈Rand0x<2}
(d) {x:x∈Rand1<x<3}
3 Using the definitions given in Section 5.2, state
whether each ofthe followingis trueorfalse:
(a) 7∈Z
(b) R − ∩Q=◦/
(c) 0.7 /∈Q (d) N + ∪Q=R +
(e) R − ∩N=◦/
(g) 5∈Q
(f) R∩Z=Z
(h) N⊂Q
4 IfA = {1,3,5,7,9,11} andB = {3,4,5,6}find
(a)A∩B
(b)A∪B
5 GivenA = {1,2,3,4,5,6},B = {2,4,6,8,10} and
C = {3,6,9} state the elements ofeach ofthe
following:
(a) A∩B
(c) A∩C
(e) A∩(B∪C)
(b)B∩C
(d)A∩B∩C
(f) B∪(A∩C)
6 Write outallthe members ofthe followingsets:
(a) A={x:x∈Nandx<10}
(b) B={x:x∈Rand0x10andxisdivisible
by3}
7 ThesetsA,BandC are given byA = {1,3,5,7,9},
B = {0,2,4,6} andC = {1,5,9} andthe universal
set,E={0,1,2,...,9}.
(a) Representthe sets onaVenn diagram.
(b) StateA ∪B.
(c) StateB ∩C.
(d) State E ∩C.
(e) StateA.
(f) StateB ∩C.
(g) StateB∪C.
8 UseVenn diagrams to illustrate the followingfor
general setsC andD:
(a)C∩D (b)C∪D (c)C∩D
(d) C∪D
(e)C∩D.
9 BydrawingVenn diagrams verifyDeMorgan’s laws
A∩B=A ∪ B and A∪B=A ∩B
10 ForsetsA = {0,1,2} andB = {3,4},draw amapping
diagramto illustrate the following relations.
Determine whichrelationsare functions.Forthose
thatare notfunctions,give reasonsforyourdecision.
(a) r:A→B,r:0→3,r:1→4,r:2→4
(b) s:A→B,s:0→3,s:0→4,s:1→3,
s:2→3
(c) t:A→B,t:0→3,t:1→4
11 IfA = {1,3,5,7} andB = {1,2,3,4},draw a
mapping diagramto illustrate the relationr :A→B,
whereristherelation‘isbiggerthan’.Israfunction?
Solutions
1 (a) {x:x∈Rand−3<x<2}
(b) {x:x∈Rand0x2}
(c) {x:x∈Rand−2x<−1}
(d) {x:x∈Rand3<x6}
(e) {x:x∈Rand−1<x<1}
2 SeeFigureS.11.
(a)
0 1 2 3 4 5 x (b) –1 0 1 x
(c)
0 1 2 3 x (d) 0 1 2 3 4 x
FigureS.11
3 (a)T (b)F (c)F (d)F
(e) T (f) T (g) T (h) T
4 (a) {3,5} (b) {1,3,4,5,6,7,9,11}
5 (a) {2,4,6} (b) {6} (c) {3,6} (d) {6}
(e) {2,3,4,6} (f) {2,3,4,6,8,10}
6 (a) {0,1,2,3,4,5,6,7,8,9}
(b) {0,3,6,9}
7 (a) SeeFigure S.12.
A
3
7
8
FigureS.12
1
5
9
B
C
0
2 4
6
(b) {0,1,2,3,4,5,6,7,9} (c) ◦/
(d) {1,5,9} (e) {0,2,4,6,8}
(f) {3,7,8} (g) {3,7,8}