show that if A is 9 collection of induct tive sets, then the intersection of
the elements of A is an inductive set?
poove the basic properties (1) and(2) oft,
a prove by induction that given nez, every nonemptr subset + of
E1,-in? has alargest element?
Explain why You can not conclude from(a) that exer r inonemptr
sebset of Z, has alargest element?
prove that the function f defined bijective? f(x)= ger ) iff iff X*9
orderpreserving bijection fiA-E63
= f(x) iff XE A-E6}
n+1 iff xeb .
show that of is in fact order preserving?
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
show there is abjective correspondence of AXB with BXA?
show that if B is not finite and BCA, then A is not finite?
If AXB is finite, does it follow that A and 13 are finite ?
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?
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
If Xty =X, then Y=0
9 X>Yandwyze X+W >ytz
O.X=0 [Hint. Computer(xto). X
I -(X) =X
1270, where x==.X
j XIX=1 ifx*0
X#O and you
P X#0 11x
t Y #0.
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