Answer:
Given,
Let
x1 =1 and x2 = 2 be two element of N
and
f(x2) = f(2)
is not one.
It
is clear that
f(1)
= 1 = f(2(1) ? 1)
f(2)
= 1 = f(2 × 1)
f(3)
= 2 = f(2(2) ? 1)
f(4)
= 2 = f(2 × 2)
f(5)
= 3 = f(2 × 2)
f(6)
= 3 = f(2(3) ? 1)
f(7)
= 4 = f(2(4) ? 1)
f(8)
= 4 = f(2 × 4)
f(9)
= 5 = f(2(5) ? 1)
f(10)
= 5 = f(2×5)
n = f(2n ? 1)
n
= f(2n)
f(2n ? 1) =
n, when n is odd
f(2n)
= n, when n is even
Let
(Co-domain of
f)
If
y is odd, of f(x) = y = f(2y ? 1)
Now
If
y is even, f(x) = y = f(2y)
Now,
Corresponding
to every
there exists
.
is onto but
not one-one.
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