   Chapter 1.2, Problem 6E

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# For the given subsets A and B of Z, let f ( x ) = 2 x and determine whether f : A → B is onto and whether it is one-to-one. Justify all negative answers. a. A = Z , B = E b. A = E , B = E

a)

To determine

Whether the mapping f:AB given by f(x)=2x is one-to one or onto or both.

Explanation

Given information:

The given function is f(x)=2x.

A= Z and B= E

Explanation:

Function f is called one-to-one, if and only if different elements of A always have different images under f.

Function f is called onto if and only if f(x)=y.

Consider the given function,

f(x)=2x

Let x1 and x2 elements in A

b)

To determine

Whether the mapping f:AB given by f(x)=2x is one-to one or onto or both.

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