discrete mathematics - chen

... one-to-one? d) Is the function onto? 11. Let f : A → B and g : B → C be functions. Prove each of the following: a) If f and g are one-to-one, then g ◦ f is one-to-one. b) If g ◦ f is one-to-one, ... one-to-one. c) If f is onto and g ◦ f is one-to-one, then g is one-to-one. d) If f and g are onto, then g ◦ f is onto. e) If g ◦ f is onto, then g is onto. f) If g ◦ f is onto and g is one-to-one,...

... spy-point, type the nospy goal | ?- nospy p. To remove p, q, and r as spy-points type the goal | ?- nospy [p, q, r]. To remove all spy-points type the goal | ?- nospyall. 120 Prolog Experiments ... string. moore(In, Out) :- start(I), execute(I, In, Out). execute(S, [ ], [ ]) :- t(S, [ ], Y, Z). execute(S, [ ], [X]) :- t(S, X, Y, Z). execute(S, [H|T], Y) :-...

... Notes Notes Discrete Mathematics Notes Discrete Notes Discrete Mathematics Notes Discrete Discrete Mathematics Notes Discrete Discrete Mathematics Notes Discrete Mathematics Discrete Mathematics Notes Discrete ... Notes Discrete Notes Discrete Mathematics Notes Discrete Discrete Mathematics Notes Discrete Discrete Mathematics Notes Discrete Mathema...

... Sean E. Corpuz Discrete Mathematics January 13, 2004 Dr. Hairong Kuang Homework #1 5. Several forms of negation are

... corresponding subset. A correspondence with these properties is called a one-to-one correspondence (or bijec- tion). If we can make a one-to-one correspondence b etween the elements of two sets, then they ... fields: the first, containing an 8-character abbreviation of an employee’s name; the second, M or F for sex; the third, the birthday of the employee, in the format mm-dd-yy (disregarding t...

... prove that the functions f and g ◦ f are one-one but g is not one-one. Solution: By definiton, it is clear that f is indeed one-one and g is not one-one. But g ◦f(x) = g(f (x)) = g(2x) = 2x 2 = ... Then (h ◦ g) ◦f = h ◦ (g ◦f) (associativity holds). 2. If f and g are one-to-one then the function g ◦ f is also one-to-one. 3. If f and g are onto then the function g ◦ f is also onto. Proof. ... m...