Problems-Functions - CmSc 180 Discrete mathematics Problems...

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CmSc 180 – Discrete mathematics Problems on Functions 1. Give an example of a function that is one-to-one but not onto 2. Give an example of a function that is onto but not one-to-one. 3. Give an example of a function that is neither one-to-one nor onto 4. Give an example of a function that is both one-to-one and onto 5. How many functions are there from A = {1,2} to B = {a, b}? Write them as sets of ordered pairs. Which are one-to-one? Which are onto? 6. Let X = {1, 2, 3, 4}, Y = {a, b, c, d}. For each of the following subsets of X x Y determine whether it is a function or not. If it is a function, determine whether it is one-to-one, onto, or both. If it is a bijection, determine its inverse function as a set of ordered pairs. A1 = {(1,a), (2,a), (3,c), (4, b)} A2 = {(1, c), (2, a), (3, b), (4, c), (2, d)} A3 = {(1, c), (2, d), (3, a), (4, b)} A4 = {(1, d), (2, d), (4, a)} A5 = {(1, b), (2, b), (3, b), (4, b)} 7. Do the following sets define functions? If so, give their domain and range: F1 = {(1, (2,3)), (2, (3,4)), (3, (1,4)), (4, (2,4))} F2 = {((1,2), 3), ((2,3), 4), ((3,3), 2)} F3 = {(1, (2,3)), (2, (3,4)), (1, (2,4))} F4 = {(1, (2,3)), (2, (2,3)), (3, (2,3))} 8. Let N be the set of all non-negative integers. Determine which of the following functions are one-to-one, which are onto, and which are one-to-one and onto: a.
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