All but two of the following statements are correct ways to express the fact that a function f is onto. Find the two that are incorrect.
a. f is onto
b. f is onto
c. f is onto
d. f is onto
e. f is onto
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Chapter 7 Solutions
WEBASSIGN F/EPPS DISCRETE MATHEMATICS
- For each of the following mappings f:ZZ, determine whether the mapping is onto and whether it is one-to-one. Justify all negative answers. a. f(x)=2x b. f(x)=3x c. f(x)=x+3 d. f(x)=x3 e. f(x)=|x| f. f(x)=x|x| g. f(x)={xifxiseven2x1ifxisodd h. f(x)={xifxisevenx1ifxisodd i. f(x)={xifxisevenx12ifxisodd j. f(x)={x1ifxiseven2xifxisoddarrow_forwardFor each of the following parts, give an example of a mapping from E to E that satisfies the given conditions. a. one-to-one and onto b. one-to-one and not onto c. onto and not one-to-one d. not one-to-one and not ontoarrow_forward10. Let and be mappings from to. Prove that if is invertible, then is onto and is one-to-one.arrow_forward
- Give an example of mappings and such that one of or is not onto but is onto.arrow_forwardLabel each of the following statements as either true or false. 3. Let , , and be mappings from into such that . Then .arrow_forwardLet a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove that f is one-to-one. Prove that f is onto if and only if a=1 or a=1.arrow_forward
- Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.arrow_forward5. For each of the following mappings, determine whether the mapping is onto and whether it is one-to-one. Justify all negative answers. (Compare these results with the corresponding parts of Exercise 4.) a. b. c. d. e. f.arrow_forwardLabel each of the following statements as either true or false. Every mapping on a nonempty set A is a relation.arrow_forward
- For each pair given in Exercise 1, decide whether is onto or one-to-one, and justify all negative answers. Exercise 1:arrow_forwardFor each of the following mappings exhibit a right inverse of with respect to mapping composition whenever one exists. a. b. c. d. e. f. g. h. i. j. k. l. m. n.arrow_forwardLabel each of the following statements as either true or false. Let g:AB and f:BC such that fg is one-to-one. Then both f and g are one-to-one.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning