by the rule
for every integer n.
(i) Is f one-to-one? Prove or give a counterexample.
(ii) Is f onto? Prove or give a counterexample.
b. Let 2Z denote the set of all even integers. That is, for some integer Define by the rule for each integer n. Is h onto? Prove or give a counterexample.
To prove is one-to-one and onto otherwise give counterexample.
Define by the rule, for all integers .
Let us suppose and assume that and now prove
So from the definition of , the expression can be written as follows-
To define by the rule, for all integers and also define whether the function is onto or not.
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