Question

f:N A where A = {0, 1} defined by f(x) = 0 if' x'is odd, = 1, if' x'is even. Then fis
one-one onto
one-one, into
many-one, onto
many-one, into​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

f : N → A where A = {0, 1} defined by

f(x) = 0 if x is odd,

= 1 , if x is even.

Then f is

• one-one onto

• one-one, into

• many-one, onto

• many-one, into

EVALUATION

Here the given function is

f : N → A where A = {0, 1} defined by

f(x) = 0 if x is odd,

= 1 , if x is even.

Now 2 , 4 ∈ N such that

f(2) = 1 & f(4) = 1

So 2 ≠ 4 but f(2) = f(4)

Hence f is not one to one function

From the given function it is clear that f maps every odd number to 0 and every even number to 1

Hence f is many one function

Here A = { 0, 1 }

Such that

f(x) = 0 if x is odd,

= 1 , if x is even.

So For every element y in A has at least one pre-image x in N such that f(x) = y

Hence f is onto function

Hence the correct option is

f is many-one , onto

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