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DLSU-CCS is in Quezon City means De La Salle University's College of Computer Studies.

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prove that n.P(n-1,n-1)=p(n,n)
prove that n.P(n-1,n-1)=p(n,n)
Let R = {(1,4), (2,1), (2,5),(2,4),(4,3),(5,3),(3,2)} on the set A = {1, 2, 3, 4, 5}. Use Warshall’s algorithm to find transitive closure of R.
show that C(n+1,k)=C(n,k-1)+C(n,k)
Let f be the function from x ={0, 1, 2, 3, 4, 5} to X defined by f(x) = 4x mod 6. Write f as a set of ordered pairs and draw the arrow diagram of f . Is f one-to-one? Is f onto?
Which of the following functions are injective? Which are surjective? a) f: Z → Z given by f(x) = x2 + 1. b) g: N → N given by g(x) = 2x. c) h: R → R given by h(x) = 5x - 1.
If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area.
Create a schematic diagram of all odd numbers from 20 to 45
(a) If x is nonnegative, then x is positive or x is 0.
4. v defined by vn = n! + 2, n ≥ 1. (a) Find v3 (b) Find Σ 4 on top , i=1 at the bottom and Vi on the right hand side of Sigma (c) Is v increasing, decreasing, non-increasing or non-decreasing?
1.b is defined by bn = n(−1)n, n ≥ 1 (a) Find Σ when 4 is on top, i=1 at the bottom and bi at the right hand side (b) Is b increasing, decreasing, non-increasing or non-decreasing?
1.b is defined by bn = n(−1)n, n ≥ 1 (a) Find Σ when 4 is on top, i=1 at the bottom and bi at the right hand side (b) Is b increasing, decreasing, non-increasing or non-decreasing?
Given ϕ2 = 5. Is ϕ increasing, decreasing, non-increasing and/or non-decreasing?
Find all substrings of the string babc.
1.Draw the digraph of the following relations. (a) R = {(1, 2), (2, 3), (3, 4), (4, 1)} on {1, 2, 3, 4} (b) R={(1, 2), (2, 1), (3, 3), (1, 1), (2, 2)} on X = {1, 2, 3}
For each relation below, determine if they are reflexive, symmetric, anti-symmetric, and transitive. (a) X= { 1, 2, 3, 4} R1={(1, 2),(2, 3),(3, 4)} (b) X = {a, b, c, d, e} R1 = { (a, a), (a, b), (a, e), (b, b), (b, e), (c, c),…
A discrete mathematics class contains I mathematics major who is a freshman, 12 mathematics majors who are sophomores, 15 computer science majors who are sophomores. 2 mathematics majors who are juniors. 2 computer science majors …
Use quantifiers and predicates with more than one vari- able to express these statements. a) There is a student in this class who can speak Hindi. b) Every student in this class plays some sport. c) Some student in this class has …
Create a schematic diagram of all odd numbers from 20 to 45
State whether the following graph g1 and g2 are isotropic or not
Find the conjunction of the propositions p and q where p is the proposition “Rebecca’s PC has more than 16 GB free hard disk space” and q is the proposition “The processor in Rebecca’s PC runs faster than 1 GHz.”
all swedish movies are serious
For each of the following compound propositions give its truth table and derive an equivalent compound proposition in disjunctive normal formal (DNF) and in conjunctive normal form (CNF). (a) (p → q) → r (b) (p ∧…
For each of the given statements: 1 - Express each of the statements using quantifiers and propositional functions. 2 - Form the negation of the statement so that no negation is to the left of the quantifier. 3 - Express the …
Translate these system specifications into English where the predicate S(x, y) is “x is in state y” and where the domain for x and y consists of all systems and all possible states, respectively. (a) ∃S(x, open) (b) ∀x(S(x…
(a) Find the inverse of 19 modulo 141, using the Extended Euclidean Algorithm. Show your steps.
A says “If B is a knight, then I am a knave”, B says nothing.
(e) Propositions 𝑝 and 𝑞 are defined on the universal set 𝑈 = {𝑞𝑢𝑎𝑑𝑟𝑖𝑙𝑎𝑡𝑒𝑟𝑎𝑙𝑠}. Let 𝑝 be the proposition “𝑥 is a square” and 𝑞 be the proposition “𝑥 is a rectangle”. If the implication is given as 𝑞 → 𝑝 , then state the conve…
Taking the long view on your education, you go to Econet Wireless Network Pvt Ltd and ask what you should do in university to be hired when you graduate. The personnel director replies that you will be hired only if you major in mathe…
Find the simplest form of given Boolean expressions using algebraic methods. i. A(A+B) + B(B+C) + C(C+A) ii. (A+|B|)(B+C) + (A+B)(C+|A|) iii. (A+B)(AC+A|C|)_+AB +B iv. |A|(A+B) + (B+A)(A+|B|)
b) Given p="Front door is open q="Back door is open" r="Light is on" s="The lift doors are open" t="The lift is moving", i) write the follow…
Detarmine whether each of these functions is a bijection from R to R
Find these values ⌊−3.1⌋
Find these values ⌊−3.1⌋
Detarmine whether each of these functions is a bijection from R to R
Let A= {1, 2, 3, 4}, and let R And S be the relations on A As follow: R = {(1,1),(1, 4),(3,2),(4,2),(4,3)} S = { (1,1),(1,2),(2,2),(3,3),(4,2),(4,4)) Then find out: 1. M𝑅𝑐 2. 𝑀𝑠̅ 3. M (𝑅∪ S)
The options available on a particular model of a car are five interior colors, six exterior colors, two types of seats, three types of engines, and three types of radios. How many different possibilities are available to the consumer?
How many different car license plates can be constructed if the licenses contain three letters followed by two digits if repetitions are allowed? If repetitions are not allowed?
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There are 5 green 7 red balls. Two balls are selected one by one without replacement. Find the probability that first is green and second is red.
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It is 8:00 AM in our 24 hour world. What time is it in a 3 hour world?
. Andy is facing West, he rotates 1260 clockwise. What direction is he now facing? (Note: A circle has 360 degrees)
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Complete the truth tables for these two Boolean expressions: (a) Output = A + B (b) Output = A + AB
6. (a) Draw the logic circuit for the following expression: AB + A(B+C) (b) Simplify the expression in 6(a) by using the rules of Boolean algebra provided in (5). (c) Draw the simplified logic gate circuit derived in (b)
2. What does it mean for two propositions to be logically equivalent?
5. Let p be the proposition “I will solve every question in this assignment” and q be the proposition “I will be fully prepared for upcoming topics” Express each of these as a combination of p and q. a. I will be fully prepared for up…
3. Give an example of a predicate P(x,y) such that ∃x∀yP(x,y) and ∀y∃xP (x, y) have different truth values.
3. Give an example of a predicate P(x,y) such that ∃x∀yP(x,y) and ∀y∃xP (x, y) have different truth values.
4. Suppose that a statement of the form ∀xP(x) is false. How can this be proved?
1. Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1), (1, 1), (1, 2), (2, 0), (2, 2), and (3, 0). Find the a) reflexive closure of R. b) symmetric closure of R. 2. Find the t…
1. Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1), (1, 1), (1, 2), (2, 0), (2, 2), and (3, 0). Find the a) reflexive closure of R. b) symmetric closure of R. 2. Find the t…
4. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(0, 0), (1, 1), (2, 2), (3, 3)} b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3),…
Define a binary relation P from R to R as follows: for all real numbers x and y, (𝑥, 𝑦) ∈ 𝑃 ⇔ 𝑥 = 𝑦^2 . Is P a function? Explain.
Define a binary relation P from R to R as follows: for all real numbers x and y, (𝑥, 𝑦) ∈ 𝑃 ⇔ 𝑥 = 𝑦^2 . Is P a function? Explain.
1. Consider the K-Maps given below. For each K- Map i. Write the appropriate standard form (SOP/POS) of Boolean expression. ii. Design the circuit using AND, NOT and OR gates. iii. Design the circuit only by using • NAND gates if …
Let R={1,1),(1,2),(2,1), (2,1), (3,3), (4,1), (5,1)} define on set A= {2,3,4,5,6}
Let R={1,1),(1,2),(2,1), (2,1), (3,3), (4,1), (5,1)} define on set A= {2,3,4,5,6}
(a) Find the inverse of 19 modulo 141, using the Extended Euclidean Algorithm. Show your steps. (b) Solve the congruence 19x ≡ 7 (mod 141), by specifying all the integer solutions x that satisfy the congruence. ≡
(a) Find the inverse of 19 modulo 141, using the Extended Euclidean Algorithm. Show your steps. (b) Solve the congruence 19x ≡ 7 (mod 141), by specifying all the integer solutions x that satisfy the congruence. ≡
(a) Use Fermat’s little theorem to compute: 4101 mod 5, 4101 mod 7, 4101 mod 11. (b) Use your results from part (a) and the Chinese Remainder Theorem to compute 4 101 mod 385. (note that 385 = 5 × 7 × 11).
(a) Use Fermat’s little theorem to compute: 4101 mod 5, 4101 mod 7, 4101 mod 11. (b) Use your results from part (a) and the Chinese Remainder Theorem to compute 4 101 mod 385. (note that 385 = 5 × 7 × 11).
Encrypt the message ATTACK using the RSA cryptosystem with n = 43 · 59 and e = 13, translating each letter into integers and grouping together pairs of integers, as done in example 11 in the textbook and in the classnotes.
Use the Well Ordering Principle to prove that any integer greater than or equal to 23 can be represented as the sum of nonnegative integer multiples of 6, 7 and 17.
Use the Well Ordering Principle to prove that any integer greater than or equal to 23 can be represented as the sum of nonnegative integer multiples of 6, 7 and 17.
Let α, β be roots of the equation x^2− 3x − 1 = 0. For each nonnegative integer n, let y_n = α^n + β^n . Show that gcd(y_n, y_(n+1)) = 1 for each nonnegative integer n.
Determine an, the number of words of length n on the alphabet {a, b, c} which do not contain the substring ab. For instance, a3 = 21 since there are 21 such words with 3 letters, namely: aaa aac aca acb acc baa bac bba b…
Let α, β be roots of the equation x^2− 3x − 1 = 0. For each nonnegative integer n, let y_n = α^n + β^n . Show that gcd(y_n, y_(n+1)) = 1 for each nonnegative integer n.
Determine an, the number of words of length n on the alphabet {a, b, c} which do not contain the substring ab. For instance, a3 = 21 since there are 21 such words with 3 letters, namely: aaa aac aca acb acc baa bac bba b…
Q1. Let {1,2,3,4,6,9} with the partial order of divisibility. Draw its Hasse Diagram Q2. [{1,2,3,4,5}, s], Draw its Hasse Diagram
[{1,2,3,4,5}, <=], Draw its Hasse Diagram.
Find (showing your reasoning) a formula for the term tn of the sequence defined by t1 = 4; tn = 2tn−1, n ≥ 2.
Consider the following two arguments: A. If Fred wanted me fired then he would go to the boss. Fred is going to the boss. Therefore Fred wants to get me fired. B. Max is a cat or Max is a mammal. Max is a cat. Therefore Max is not a…

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Question ID: mtid-5-stid-8-sqid-3223-qpid-1922