Proficiency #17. [Images and Inverse] Let f : S → T be a function, and let A and B be subsets of S. Prove or give a counterex- ample to the statement f(An B) = f(A) N f(B).

ab Let f and g be functions defined as follows: 2 ƒ = {( − 19, − 2), ( – 18, − 1), ( – 17, 3). (- 16, ₂).(-15,3)} 3 9 = {( − 18 19,- -7).(-18, 1). (-17, 3). (-16, ).(-15,0)} 4 10 Compute the indicated value. If the value does not exist, enter DNE. (i) (g+g)(15) = (ii) (fg)(16) = (iii) (ff)(19) = (iv) (4) 18) = > Next Question G Search or type URL ← % 6 esc 1 Q @ 2 W #3 Q E D $ 4 R 5 T

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Proficiency #15. [Properties and Defintions of Functions] Let A and B be sets, and let f, g C A × B be functions. Prove that f ng is a function.