discrete mathematics - j saxl (1995) ww

... s, n ∈ Z. Take an (r + s)-set and split it into an r-set and an s-set. Choosing an n-subset amounts to choosing a k-subset from the r-set and an (n −k)-subset from the s-set for various k. 16 CHAPTER ... −I A n ) =  J {1, ,n} (−1) |J| I A J , Summing over s ∈ S we obtain the result   A 1 ∪ ··· ∪ A n   =  J {1, ,n} (−1) |J| |A J |, which is equivalent to the required result. Ju...

Ngày tải lên: 12/05/2014, 01:52

...

Ngày tải lên: 12/05/2014, 02:28

... For example, try out the following goals. | ?- X is 5 + 7. | ?- X is 5 - 4 + 2. | ?- X is 5 * 45. | ?- X is log(2.7). | ?- X is exp(1). | ?- X is 12 mod 5. The expression on the right ... | ?- p(a). Perform each test separately with only the given clauses as input. a. p(b). b. p(c). p(a) :- p(b). p(a) :- p(b). p(a) :- p(c). p(a) :-...

Ngày tải lên: 21/02/2014, 09:20

... 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...

Ngày tải lên: 08/03/2014, 12:20

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

Ngày tải lên: 27/03/2014, 11:56

... 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 ... important method of counting: we established a corre- spondence between the objects we wanted to count (the subsets) and some other kinds of objects that we can count easily (the numbers...

Ngày tải lên: 31/03/2014, 12:20

... t 1 , t 2 , . . . , t ℓ then k = ℓ and for each i, 1 ≤ i ≤ k, there exists j, 1 ≤ j ≤ k such that p i = q j and s i = t j . 16 CHAPTER 1. PRELIMINARIES Proof. We prove the result using the strong ... the remainder when a · b is divided by m. (a) Prove that i (mod n) + j (mod n) = i + j (mod n) and i (mod n) · j (mod n) = ij (mod n). (b) In Z 5 , solve the equation 2x ≡ 1 (mod 5)....

Ngày tải lên: 31/03/2014, 12:20

Ngày tải lên: 31/03/2014, 15:57

... 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,...

Ngày tải lên: 31/03/2014, 15:58