Question

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4. Let A- (0,1,2,3,4) and f:A and f(f(n)) A where f(n) 2n mod 5. Construct a table with values for n, f(n)

Answer 1

The required table is shown below.

Explanation:

The given set is

`A=\{0,1,2,3,4\}`

It is given that

`f:A\rightarrow A`

where,
`f(n)=2n(mod 5)`.

We need to construct a table with values for n, f(n) and f(f(n)).

The elements of set are 0,1,2,3 and 4 so these are the values of n.

At n=0,

`f(0)=2(0)(mod 5)=0(mod 5)=0`

`f(f(0))=f(0)=0`

At n=1,

`f(1)=2(1)(mod 5)=2(mod 5)=2`

`f(f(1))=f(2)=2(2)(mod 5)=4(mod 5)=4`

At n=2,

`f(2)=2(2)(mod 5)=4(mod 5)=4`

`f(f(2))=f(4)=3`

At n=3,

`f(3)=2(3)(mod 5)=6(mod 5)=1`

`f(f(3))=f(1)=2`

At n=4,

`f(4)=2(4)(mod 5)=8(mod 5)=3`

`f(f(4))=f(3)=1`

Therefore the required table is

n f(n) f(f(n))

0 0 0

1 2 4

2 4 3

3 1 2

4 3 1