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Standard VI
Mathematics
Planes
ntLet A be a ...
Question
ntLet A be a finite set. If f:A→A is an onto mapping, show that it is one-one also.n
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Q.
Let
A
be a finite set, If
f
:
A
→
A
is onto. Show that
f
is one-one
Q.
Let A be a finite set of size n the number of power set of AxA is
Q.
Let C be the set of complex numbers. Prove that the mapping
f
:
C
→
R
given by
f
(
z
)
=
|
z
|
,
z
ϵ
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is neither one-one nor onto.
Q.
Let
A
and
B
be two finite sets having
m
and
n
elements respectively such that
m
≤
n
. A mapping is selected at random from the set of all mappings from
A
to
B
. The probability that the mapping selected is an injection, is
Q.
Let A and B be two sets with a finite number of elements. Assume that there is injective mapping from A to B and that there is an injective mapping from B to A. Prove that there is a bijective mapping from A to B.
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