For each n N, let Aₙ = ≤ft\{ (n+1)k/k k N \} and X = ₙ N} Aₙ. A mapping f: X arrow N defined by f(x) = x, x X, is

Correct Answer is : one - one but not onto

Correct Answer is : one - one but not onto

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TS EAMCET 11-Sep-2020 Shift 2 Solved Paper

Section: Mathematics

Question : 2 of 160

Marks: +1, -0

For each

n \in N

A_n = \left\{ \frac{(n+1)k}{k} k \in N \right\}

X = \bigcup_{n \in N} A_n

f: X \rightarrow N

f(x) = x, \forall x \in X,

Solution:

Given that,

A_n = \left\{ (n+1) k \mid k \in N \right\}

n = 1, A_1 = \left\{ 2k \mid k \in N \right\}

for,

k = 1, 2, 3 \ldots A_1 = \left\{ 2, 4, 6, 8, \ldots \right\}

\; \; n = 2, A_2 = \left\{ 3k \mid k \in N \right\}

for

k = 1, 2, 3, \ldots \; \; A_2 = \left\{ 3, 6, 9, \ldots \right\}

n = 3, A_3 = \left\{ 4k \mid k \in N \right\}

for

k = 1, 2, 3, \ldots A_3 = \left\{ 4, 8, 12, \ldots \right\}

Now,

X = \bigcup_{n \in N} A_n

X = A_1 \cup A_2 \cup A_3 \ldots

\; \; X = \left\{ 2, 3, 4, 5, 6, \ldots \right\}

Here,

f: X \rightarrow N

and

f(x) = x \forall x \in X

\because f(x)

is linear function i.e., it is one-one function but there is no value of

x

in domain where

f(x) = 1

\therefore f(x)

is not onto function.

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