Transcribed Text
7
show that if A is 9 collection of induct tive sets, then the intersection of
the elements of A is an inductive set?
b
poove the basic properties (1) and(2) oft,
8
a prove by induction that given nez, every nonemptr subset + of
E1,in? has alargest element?
b
Explain why You can not conclude from(a) that exer r inonemptr
sebset of Z, has alargest element?
9
prove that the function f defined bijective? f(x)= ger ) iff iff X*9
nt/ x=90
orderpreserving bijection fiAE63

6
Sir
f(x)
= f(x) iff XE AE6}
n+1 iff xeb .
show that of is in fact order preserving?
C
poove that Leb A be afinite set and suppose that BCA IFB is
a aproper subset of A then the cardinality of (Bis strictlyless than the cardinality
of A?decead
/
show there is abjective correspondence of AXB with BXA?
2
show that if B is not finite and BCA, then A is not finite?
3
If AXB is finite, does it follow that A and 13 are finite ?
4
a Let A=E1, win? show there is abijection of p(A)With the cartesian product **,
where xis the two, element set X=40,13?
6
show that if A is finite, then p(A)is finite?
5 poove that following "laws of algebra 11:
6 prove the following "laws of inequalities
a
If Xty =X, then Y=0
9 X>Yandwyze X+W >ytz
6
O.X=0 [Hint. Computer(xto). X
6
X>oand. you
xty7oand x.y70
C
 O=O
C
OXYOESKKO
I (X) =X
d OXSYEDKCY.
CO
e
x>yandzco
x7D111*==X
DX#O
1270, where x==.X
)KOCZ.
h
h
i Y=1
or bothnegative.
th positive
j XIX=1 ifx*0
Dx>o 21x70.
U
1x4940
K
XII=X
1/X< 1/Y
I
X#O and you
) KXYFO
m
11
(XIY)
P X#0 11x
9
2/1w1Z) =zwifwitzo
t
770.
s =
t Y #0.
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