30
Solutions to Exercises
Exercises 2.1
1.
(a) [BBJ{
J5,
J5}
(b) {I, 3, 5,15,
1, 3, 5, 15}
(c) [BB] {O,
~}
(Although ±v'2 are solutions to the equation, they are not rational.)
(d) {1,0,1,2,3}
(e) This is the empty set. There are no numbers less than
4
and
bigger than +4.
2. (a) [BB] For example, 1 + i, 1 + 2i, 1 + 3i,
8  5i and 17  43i.
(b) For example, {I  2v'2, 1  5v'2, 1  7v'2, 316  2v'2 and 394 
7v'2}.
(c)
If
x
=
0,
y
= ±5
and
x/y
=
o. If
x
=
1,
y
=
±VU,
and
=
±l/VU
=
±VU/24.
x
=
2,
y
=
±.J2i and
= ±2.J2i/2l.
Five elements of the given set are 0,
VU/24,
VU/24,
2.J2i/2l and 2.J2i/2l.
(d) {2, 3, 5, 6, 8}.
3. (a) [BB] {I, 2}, {I, 2, 3}, {I, 2, 4}, {I, 2, 3, 4}
(b) 0, {I}, {2},{1,2}
(c) 0, {I}, {2}, {3}, {4}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,3,4 },{2,3,4}
(d) {3}, {4}, {1,3}, {1,4},{2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4},{1,2,3,4}
~)
{1,2,3}, {1,2,4}, {1,2,3,4}
(t) 0, {I}, {2}.
4. [BB] Only (c) is true. The set
A
contains one element,
{a, b}.
5. (a) [BB] True. 3 belongs to the set {I, 3, 5}.
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 Summer '10
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 Graph Theory

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