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Unformatted text preview: x R y iﬀ b x 3 cb y 3 c . What is . . . (a) 5 R 7 (b)  R (c)  R =  R (d) (2 , 4) ∈ R 4. Consider the function f : R 7→ R , where f ( x ) = 1 + sin x . (a) What it the domain of f ? (b) What is the codomain of f ? 1 (c) What is the range of f ? (d) Is f one-to-one? (e) Is f onto? (f) Is f invertible? If not, deﬁne a new function f in the same spirit as f , but that is invertible? 5. Deﬁne a one-to-one and onto function g : Z 7→ Z + . 6. Consider two relations A and B on a set S . • If A and B are reﬂexive, must A ◦ B be reﬂexive? Prove your answer. • If A and B are symmetric, must A ◦ B be symmetric? Prove your answer. 2...
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