Solved: Robyn decides to organize a hiking trip and invites her friends - Dylan, Linda and Dominic to join her. On the days leading to the hike, her three friends say the following:Two Days Before the hike:Dylan: Dominic is going to the hike. Dominic: Linda is not going to the hike.Linda: Dylan will go to the hike if, and only if, I do.The Day Before the hike:Dylan: Linda will go to the hike if, and only if, I don't go. Dominic: An even number out of the three of us are going to the hike.Linda: Dylan is going to the hike.The Day of the hike:Dylan: It is not yet 2020. Dominic: Dylan will go to the hike if, and only if, I do.Linda: At least one of the three of us is not going to the hike. Robyn also knows that out of Dylan, Dominic, and Linda:One of them never lies.One lies on days of the month that are divisible by 2, but is otherwise truthful.The remaining one lies on days of the month that are divisible by 3, but is otherwise truthful.Can you figure out who is going to attend?

bit is either 0 or 1: a byte is a sequence of 8 bits. Find (a) the number of bytes that can be formed (b) the number of bytes that begin with 11 and end with 11 (c) the number of bytes that begin with 11 and do not end with 1…

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4. Let A and B be sets. Prove the commutative laws from Table 1 by showing that a) A ∪ B = B ∪ A. b) A ∩ B = B ∩ A.

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Let R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)} R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)} is a relation on set A={1,2,3,4} A={1,2,3,4} Suppose a Rn b means that there is a path of length n from a to b Which of the elements are …

Answer the following items. Show your complete answer on a separate sheet of paper. Prove that the following sentences are tautologies. 1. p →p 2. p → (p V q) 3. [p Λ (p → q)] → q 4. p V ~p 5. q → (p V ~p) 6. ~p…

Show that the relation R = ∅ on a nonempty set S is symmetric and transitive but not reflexive.

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Theorem 2:- An (m,n) encoding ∅ corrects K or fewer errors if and only if the minimum distance between encoded words is atleast 2K+1 Proof:- Suppose that ∅ corrects K or fewer errors x is an encoded word of distance 1≤j≤k …

One hundred students were asked whether they had taken course in any of the three areas, CSE, ME and EE. The results were. 45 had taken CSE, 38 had taken ME, 21 had taken EE, 18 had taken CSE and ME, 9 had taken CSE and…

Consider a Boolean expression Ex,y,z=xzv(y^z). Find disjunctive and conjunctive normal form.

For each stall there are 3 ways to exhibit one of three animals. Since there are 10 stalls, by Combinatorial Product Rule, the number of ways of arranging the exhibition is equal to 3\cdot 3\cdot\ldots\cdot 3=3^{10…

There are 10 stalls for animals in an exhibition. Three animals; lion, pussycat and horse are to be exhibited. Animals of each kind are not less than 10 in number. What is the possible number of ways of arranging the exh…

Show that the following logical equivalences hold for the Peirce arrow ↓, where P ↓ Q ≡ ∼(P ∨ Q). a. ∼P ≡ P ↓ P b. P ∨ Q ≡ (P ↓ Q) ↓ (P ↓ Q) c. P ∧ Q ≡ (P ↓ P) ↓ (Q ↓ Q) H d. Write P → Q using Peirce arrows on…

Obtain the Conjunctive Normal Form of (x^y) V (-x^y)

Define and give examples of injective surjective and bijective functions. Check the injectivity and surjectivity of the following function f: NN given by f(x)=x2

A school organized a book fair and in this book fair a book seller is selling his books under the following rules: There are three different packages available. First package contains 2 Islamic books, 2 Science books and 2 Geography…

The argument is p→~q,~r→p,q|–r in true table in mathematical foundations of computer science

How many license plates can be made using either two or three letters followed by either two or three digits?

Show ((p ∨ q) ∧ ¬(¬p ∧ (¬q ∨ ¬r))) ∨ (¬p ∧ ¬q) ∨ (¬p ∧ ¬r) is tautology, by using replacement process.

I come to class whenever there is going to be a quiz this statement is inverse converse and contarpositve?

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Let an denote the number of surjective (onto) functions f : {1, 2, . . . , n} −→ {1, 2, 3} such that f(1) < f(2). Give a Θ estimate for an.

A committee of 8 is to be formed from 16 men and 10 women. In how many ways can the committee be formed if i) there are no restrictions. ii) there must be 4 men and 4 women. iii) there should be an …

A committee of 8 is to be formed from 16 men and 10 women. In how many ways can the committee be formed if i) there are no restrictions. ii) there must be 4 men and 4 women. iii) there should be an even number of women. …

solve the recurrence t(n)=(t(n/2)^2) assuming t(1)=1

list the ordered pairs in the equivalence relations R induced by these partitions of p { {1} , {3} , { 2,4,5,6} rt he set of { 1,2,3,4,5,6}

Suppose there are 10 male and 6 female professors to teach Discrete mathematics. In how many ways a student can choose Discrete mathematics professor.

Let R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)} R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)} is a relation on set A={1,2,3,4} A={1,2,3,4} Suppose a Rn b means that there is a path of length n from a to b Which of the elements are …

The argument is p→~q,~r→p,q|–r in true table in mathematical foundations of computer science

Obtain the Conjunctive Normal Form of (x^y) V (-x^y)

Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c,…

Draw a simple, undirected graph yourself, the vertices are connected with each other including 8 vertices and 14 edges. Find the shortest path from two arbitrary vertices: a) The weight of each edge is 1. b) Self-weighting for…

Let A, B, C, D denote, respectively, art, biology, chemistry, and drama courses. Find the number N of students in a dormitory given the data: 12 take A, 5 takeAand B, 4 takeB and D, 2 take B, C,D, 20 take B, 7 takeAand C, 3 t…

The following formulas have been abbreviated based on the common abbreviation rules. Follow the steps below and translate the formulas into good English. · Step 1: Re-add the omitted brackets. · Step 2: If necessary, con…

State TRUE or FALSE justifying your answer with proper reason. a. 2𝑛^2 + 1 = 𝑂(𝑛^2 ) b. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 ) c. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 log 𝑛) d. 3𝑛^2 + √𝑛 = 𝑂(𝑛 + 𝑛√𝑛 + √𝑛) e. √𝑛 log 𝑛 = 𝑂(𝑛)

solve the following recurrence relations a. 𝑇(𝑛) = 𝑇( 𝑛/4) + 𝑇( 𝑛/2 ) + 𝑛^2 b. T(n) = T(n/5) + T(4n/5) + n c. 𝑇(𝑛) = 3𝑇( n/4 ) + 𝑐𝑛^2 f. 𝑇(𝑛) = (𝑛/𝑛−5) * 𝑇(𝑛 − 1) + 1 g. 𝑇(𝑛) = 𝑇(log 𝑛) + log 𝑛 h. 𝑇(𝑛) = 𝑇 (𝑛^ 1/ 4) + 1 i. 𝑇(𝑛…

How many positive integers less than 100 is not a factor of 2,3 and 5?

A pet store keeps track of the purchases of customers over a fours hour period. The store manager classifies purchases as containing a dog product, a cat product, a fish product, or product for a different kind of pet. He found! …

For the relation R = {(p,p) ,(q,p),(q,q),(r,r),(r,s),(s,s) ,(s,m) ,(m,m)} 1.Using warshall algorithm find the transitive closure R* of R 2.write matrix representation of R* 3.Check whether the relation of R* is an equiv…

Write the converse, inverse, and contrapositive of the following conditional propositions. (Hint: If applicable, write each conditional proposition in standard form first.) a. Rose may graduate if she has 120 hours of OJT credits. …

How many different plates are there that involve 1, 2 or 3 letters followed by 1, 2, 3 or 4 digits? How many 2 digit or 3-digit numbers can be formed using the digits 1, 3, 4, 5, 6, 8 and 9 if no repetition is allowed?

The following table shows the income distribution of 600 families. Find the minimum income of the riches 30% families. Also the limits of income of middle 50% of families, to the nearest rupees. Income Below 75 75- 1…

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Show that the relation R on Z × Z defined by (a, b) R (c, d) if and only if a + d = b + c is an equivalence relation. Note: A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive.

Let 8Z be the set of all integers that are multiples of 8. Prove that 8Z has the same cardinality as 3Z, the set of all integers multiples of 3.

We assume the question is: What is mathematical foundation for computer science? Solution: The mathematical side concentrates on areas where computers are used, or which are relevant to computer science, namely algebra, general topo…

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(a) By the definition of piece arrow- P\downarrow Q=P↓Q= ~(P\lor Q)(P∨Q) P\downarrow QP↓Q =~(P\lor P)(P∨P) We have derived that P\downarrow PP↓P is logically equivalent with ~P ~P=P&b…

Show that the following logical equivalences hold for the Peirce arrow ↓, where P ↓ Q ≡ ∼(P ∨ Q). a. ∼P ≡ P ↓ P b. P ∨ Q ≡ (P ↓ Q) ↓ (P ↓ Q) c. P ∧ Q ≡ (P ↓ P) ↓ (Q ↓ Q) H d. Write P → Q using Peirce arrows on…

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Given the following 2 premises, 1. 𝑝 → (𝑞 ∨ 𝑟) 2. 𝑞 → 𝑠 Prove 𝑝 → (𝑟 ∨ 𝑠) is valid using the Proof by Contradiction method.

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Let R1 and R2 be symmetric relations. Is R1 ∩ R2 also symmetric? Is R1 ∪ R2 also symmetric?

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An electrician charges a base fee of $70 plus $50 for each hour of work. Create a table that shows the amount the electrician charges for 1,2,3, and 4 hours of work. Let x represent the number of hours and y represent the amount charg…

Given The Following 2 Premises, 1. 𝑝→(𝑞∨𝑟) 2. 𝑞→𝑠 Prove 𝑝→(𝑟∨𝑠) Is Valid Using The Proof By Contradiction Method. [Hint: Use A Combination Of Equivalence Laws And Rules Of Inference To Solve This Question]

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Construct the network who's activity and the relationship Activity:A,C,D can start simultaneously Activity:E>B,C;F,G>D;H,I>E,F;J>I,G;K>H;B>A

Construct the network who's activity and the relationship Activity:A

Construct a relation on the set {a, b, c, d} that is a. reflexive, symmetric, but not transitive

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