Solved: (I) A relation R on a set S is called irreflexive, if no element in S is related to itself, that is if for every a in S, (a, a) is not in R. Which of the relations in Q. No. 5 is irreflexive?

1. Three departmental committees have 6, 12, and 9 members with no overlapping membership. In how many ways can these committees send one member to meet with the president? 2. Two dice are rolled, one blue and one red. How ma…

Basic Counting Principle 6. How many different car license plates can be constructed if the licenses contain three letters followed by two digits if: a.) Repetitions are allowed; b.) repetitions are not allowed. 7. Two d…

Find the generating function of recurrence relation an+1_an=3n ,n less than 0 where ao=1

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Show that ¬ (P\iff⟺Q)\iff⟺(P V Q) Λ ¬(P Λ Q) \iff⟺(P Λ ¬Q) V (¬ P Λ Q) without using truth table

Design a single error correcting code for m=3 & n=7

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Let g be a function from Z+ (the set of positive integers) to Q (the set of rational numbers) defined by (x, y) element of g iff y = (g is a subset of Z+ mapped with Q) and let f be a function on Z + defined by (x, y) element of f iff…

Let A = {1,2,3,4,6,8,9,12,18,24} be a non-empty set and R be the partial order relation of divisibility defined on A, i.e., If (a,b) ε A, then a divides b i. Draw the Hasse diagram of R. ii. Find the Maximal and Minimal elements in…

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an-3an-1-4an-2=4.3n

Solve the Recurrence relation an-3an-1-4an-2=4.3n where a0=1,a1=2

Solve the Recurrence relation an-3an-1-4an-2=4*3n where a0=1,a1=2

Out of 300 students taking discrete mathematics, 60 take coffee, 27 take cocoa, 36 take tea, 17 take tea only, 47 take chocolate only, 7 take chocolate and cocoa, 3 take chocolate, tea and cocoa, 20 take cocoa only, 2 take tea, coffee…

Let W ={1,2,….,8} Q = {2,4,6,8,10}, Y = {1,2,4,5,6,8,9}. Evaluate: W union Y (2 marks) Q intersection Y (2 marks) Set Difference P minus Y (2 marks) (W intersection Q) union Y

Let p, q, and r be the propositions: p = "the flag is set" q = "I = 0" r = "subroutine S is completed" Translate each of the following propositions into symbols, using the letters p, q, r and logical conn…

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Let U = {l, 2, 3, 4, 5, 6, 7, 8, 9, and 10} be a universal set. Let A, B, C such that A= {l, 3, 4, 8}, B = {2, 3, 4, 5, 9, 10}, and C = {3, 5, 7, 9, 10}. Use bit representations(computer representation) for A, B, and C together with …

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Let f:R\to→ R be f(x)= x/1+|x| a) Is f everywhere defined? If not, give the domain. b) Is f onto? If not give the range. c) Is f one-to-one? Explain. d) Is f invertible? If so, what is f-1?

Consider the following relations on the set A={1,2,3,4,5}. a) R1={(1,1), (1,2), (3,3), (3,2)} b) R2={(1,1), (2,2), (3,2), (4,5), (5,2)} c) R3={(1,4), (2,5), (3,3), (4,2), (5,2)} State, with reasons, for a), b), c) whether the rela…

Question #221673 Say for each of the posets represented by the given Hasse-diagram whether the poset is i) a lattice ii) a complemented lattice iii) a Boolean algebra Give reasons for your answers

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Branches and chords may change according to the spanning tree.”-- Do you agree? Justify your answer

Given the following recurrence relation (M). an = −4an−1 + 5an−2, a0 = 2, a1 = 8 The solution of (M) is: a. an = 3 − (−5) n b. an = 3 + (5) n c. an = (3) n − 5 d. None of these

ACTIVITIES/ASSESSMENT: A. Tell if the following statements are propositions or not. 1. Study hard! 2. The Apple Macintosh is a 16-bit computer. 3. 1 is an even number. 4. Why are we here? 5.8+7=13 B. p is "x …

Question #222539 1. Let p and q be the propositions “Swimming at the New Jersey shore is allowed” and “Sharks have been spotted near the shore,” respectively. Express each of these compound propositions as an English sentence. a) ¬…

let z be the set of integers and R be the relation on Z defined as: aRb if and only if 1+ab>0 then

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Express each of these statment using quantifires : a) every student in this classes has taken exactly two mathematics classes at this school. b) someone has visited every country in the world except Libya

Describe the Hasse diagram formed by the Relation "x is a divisor of y" for the set A = {1, 3, 6, 12, 24, 48}

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In the following Statement: " If the BIOS test runs fine, the CPU and motherboard must be OK. If the CPU and motherboard and memory are all OK, then there must be a flaw in the OS. The BIOS test runs fine and the memory is OK. …

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A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point is drawn for each element of the poset, and line segments ar…

Describe the Hasse diagram formed by the Relation "x is a divisor of y" for the set A = {1, 3, 6, 12, 24, 48}

For the following relation on the set {1,2,3,4,5,6,7,8,9,10,11,12}.

Describe the Hasse diagram formed by the Relation "x is a divisor of y" for the set A = {1, 3, 6, 12, 24, 48}

Find the number of distinct permutation of the word 'programmer '

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complete \space question \space is \space \\ Let \space f:R→R \space is \space defined \space by \space f(x)= \space \frac{x}{1+∣x∣}.\\ \space Then \space…

Let f :R \to→ R be f (x) =x /(1+|x|)

2) Translate the given statements into propositional logic using the propositions provided You are eligible to be the President of the USA if and only if you are at least 35 years old, were born in the USA, or at the time of your …

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Let A= {0, 1, 2, 3} and define relations R, S and T on A as follows: R= { (0,0),(0,1),(0,3),(1,0),(1,1),(2,2),(3,0),(3,3)} S= {(0, 0),(2,2),(1,1), (0, 2), (0, 3), (2, 3),(2,2)} T= {(0, 1), (2, 3),(0,0),(2,2),(1,0),(3,3),(3,2)} i. Is R…

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Determine how many bit strings of length 5 can be formed ,where three consecutive 0s are not allowed

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determine how many bit strings of length can be formed, where three consecutive 0s are not allowed

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Determine whether each of the following compound propositions is satisfiable. Justify your answer. 1. (a) (pv-g)^(-pVg)^(-p^ g) (b) ()^(-)^(-p)^(---) (c) (pvqv-r) ^ (pv-gv-8) ^ (pv-rv-8)^(-pv-gv-) A (pvqV-s)

2) Construct a circuit using NOT gates, OR gates and AND gates of the following proposition (P and -r)or(-q and r)

3) Using basic propositional equivalence (which we did in the class) show that (pr) ^ (4) and (pvg) → are logically equivalent. (Don't use truth table for this problem) O U

2.1 Differentiate f(x) = (2x3 + 3x2 )(x2 + 5x3 +5) using product rule. (5) 2.2 Differentiate f(x) = (8x 3 + 4x )(2x 2 +5) using product rule. (5) 2.3 Differentiate f(x) = 5𝑥³+7𝑥 2𝑥²−4𝑥+5 using quotient rule. (5) 2.4 Diffe…

2fn-f(n-2) = fn+1 for n>3

(I) A relation R on a set S is called irreflexive, if no element in S is related to itself, that is if for every a in S, (a, a) is not in R. Which of the relations in Q. No. 5 is irreflexive?

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Question ID: mtid-5-stid-8-sqid-2861-qpid-1418