Discrete Math (7) (bonus) Give a proof of the following equivalence following the pattern of proof...
Discrete Math- Check my work and explain if I got anything wrong 7. Prove that the following formulas Fi and F2 are equivalent: F1:-(3x (p(x) (Fy (g(y) 1-r(x, y))))) F2: Vx (p(x) → (Vy (q(y) +r(x, y)))) Clearly label each equivalence used in your proof. 7. = x + 7 (pc) n/7ylfly) 170 (x,y)))) 7J x PC) = HX7 P05 = YG pux) v 7 (7y (q (y) 17 r(x, y))) 1 paq=1p uq = kx (7 p.) v (Vy...
Discrete Math Consider the following directed graph. Give the indegree of each vertex.
please answer the question using 0 & 1 instead of T & F 7. (10) Give a direct proof and an indirect proof of the following: 7. (10) Give a direct proof and an indirect proof of the following:
(Discrete Math) Read the following combinatorial proof, and write a theorem that we proved. Explain it in details. We count the number of k+1 element subsets of [n+1]. On one hand, it is clearly C(n+1,k+1). On the other hand, we can count these subsets in two steps. First we count the subsets that contain the number n+1. Since have to choose another k elements from {1,2,...,n} for it to make a k+1-element set, the number of these is C(n,k). Then...
discrete math Need 7c 9ab 10 15 16 17 (7) Consider the following matrices. Compute the following matrices A=[ ]B=[ 1 c-[! (a) CA (b) BAA (c) AOC (9) Determine if the following statements are True or False. If the statement is False, explain why. (a) Consider A={1,2,3,4,5). Do A1 = {1,3,5}, A2 = {2,4}. (i) Show that P ={A1, A2} forms a partition of A. (ii) Construct the matrix of the relation R corresponding to P (b) Consider A...
Question 7 Classify each of the following sets as finite, countable infinite, or uncountable (no proof is necessary): A=0 B = {2 ER: 0 < x < 0.0001} C=0 D=N E = {R} F= {n EN:n <9000} G=Z/5Z H = P(N) I= {n €Z:n > 50 J=Z Bonus: Give an example of a set with larger cardinality then any of the above sets.
Discrete Math Question (Q26, P55, Textbook: Mathematical Structures for Computer Science 7e): Give English language translations of the following wffs if:
How to do this problem for discrete math. Use the rules of inference to show that if V x (Ax) v α刈and V xứcAx) Λ α where the domains of all quantifiers are the same. Construct your argument by rearranging the following building blocks. ) → Rx)) are true, then V x("A(x) → A is also tr 1. We will show that if the premises are true, then (1A(a) → Pla) for every a. 2. Suppose -R(a) is true for...
Give an epsilon delta proof for the following limit: as x—>3 lim(6x-7)=11
Discrete Math Give a big-Theta estimate for the number of additions in the following algorithm a) procedure f (n: integer) bar = 0; for i = 1 to n^3 for j = 1 to n^2 bar = bar + i + j return bar b) Consider the procedure T given below. procedure T (n: positive integer) if n = 1 return 2 for i = 1 to n^3 x = x + x + x return T(/4) + T(/4) +...