Solved: Every function is a relation, but the converse is not true.”--True or false? Justify with an example.

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

What is degree of a vertex in a graph?

Express the negations of each of these statements so that all negation symbols immediately precede predicates. ∃x∃y(Q(x, y) ↔ Q(y, x))

Draw the Venn diagrams for each of these combinations of the sets A, B, C, and D. *A̅ ∪ B̅ ∪ C̅ ∪ D̅

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}

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

Express each of these statement using quantifires : No one has climbed every mountain in the Himalayas

Express each of these statement using quantifires : every movie actor has either been in a movie with Kevin Bacon or has been in a movie with someone who has been in. a movie with Kevin Bacon.

3.3 In a class of 100 learners, 80 do Mathematics and 35 do Physics. If x learners do Mathematics and Physics, and y learners do neither Mathematics nor Physics, find the greatest possible value of y.

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. …

Express 2x+1 / x(x+1) in partial fractions and hence find the general solution of the differential equation x(x+1)dy/dx = y(2x+1) expressing y explicitly in terms of x.

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 '

Draw the Venn diagrams for each of these combinations of the sets A, B, and C. a) A ∩ (B − C) b) (A ∩ B) ∪ (A ∩ C) c) (A ∩ B) ∪ (A ∩ C)

The number of elements in the Power set P(S) of the set S = { { Φ} , 1, { 2, 3 }} is?

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 …

Suppose the city of MISSISSAUGA has a contest where they arrange the letters of their city name in a particular order. The city residents have to guess which order the city has chosen, and the winner gets $10 000. The rules allow peop…

Determine whether the function f(x) = x^2 + 3x + 2 from Z to Z is a bijective function.

Solve the recurrence by master's method. a) T(n) = 3T[n/4)+ cn^2 b) T(n)=T[2n/3)+1

Solve the recurrence by substitution method. T(n) = 2T (n/2)+n-1 and T (1) =1.

Translate the following English sentences into Propositional Logic. Let: C A bird can fiy F A bird has wings a) If Bird has wings, then bird can fly. b) If bird has no wings, then it can't fly.

Translate the following Propositional Logic to English sentences. Let: E-Lion is eating H=Lion is hungry a) E-H b) EA-H c)-(H-E)

Is (p q) > I(p>q)> q] a tautology? Why or why not?

Solve the recurrence by substitution method. T(n) = 2T (n/2)+n-1 and T (1) =1.

Draw the Venn diagrams for each of these combinations of the sets A, B, C, and D. a) (A ∩ B) ∪ (C ∩ D) b) A c U B c U Cc U Dc c) A − (B ∩ C ∩ D) d) A ⊕ B

How many strings of six lowercase letters from the English alphabet contain: i.The letter a? ii. The letters a and b? iii. The letters a and b in consecutive positions with a preceding b, with all the letters distinct? iv. The letters…

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…

Determine whether the relation R on the set of all people is irreflexive, where (a, b) ∈ R if and only if : i) a and b were born on the same day. ii) a has the same first name as b. iii) a and b have a common grandparent

Question No 05: [07 marks] Let f (x) = ax + b and g(x) = cx + d, where a, b, c, and d are constants. Determine necessary and sufficient conditions on the constants a, b, c, and d so that f ◦ g = g ◦ f

Find the domain and range of these functions. i. The function that assigns to each pair of positive integers the first integer of the pair b) the function that assigns to each positive integer its largest decimal digit ii. The functio…

Briefly answer the following short questions 1) Determine if the following argument is valid and explain why. Every CS major takes CMSC203. Mr. Ali is taking CMSC203, therefore he is a CS major. 2) What is the time complexity (in …

Prove that for every positive integer n. 1.2.3+2.3.4++ n(n+1)(n+2) = n(n+1)(n+2)(n+3)/4.

How many strings of six lowercase letters from the English alphabet contain: i.The letter a? ii. The letters a and b? iii. The letters a and b in consecutive positions with a preceding b, with all the letters distinct? iv. The lett…

Determine whether the function f(x) = |4x| from Z to Z is a bijective function.

A boy has 10 red balls, 20 blue balls,25 black balls ,and 30 pink balls .He select ball at random without looking at them .calculate the minimum number of balls he must select to be sure that at least 6 balls of the same color .

1) Draw the Hasse diagram for inclusion on the set P(S), where S = {a, b, c, d} 2) Let S = {1,2,3,4} with lexicographic order "<=" relation a. Find all pairs in S x S less than (2, 3) b. Find all pairs in S x S greater than…

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

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

Determine whether the given relation is reflexive, symmetric, transitive, or none of these. R is the ”greater than or equal to” relation on the set of real numbers: For all x, y ∈ R , xRy ⇐⇒ x ≥ y

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

Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter R in the set of all months of the year.

Let p and q be the propositions defined as below. p : It is below freezing. q : It is snowing.

Show that a complete graph with n vertices has n(n -1) 2 edges

Show that for any real number x, if x2 is odd, then x is odd.

Let p, q and r be statements. Use the Laws of Logical Equivalence and the equivalence of → to a disjunction to show that: ∼ ((p ∨ (q →∼ r)) ∧ (r → (p∨ ∼ q))) ≡ (∼ p ∧ q) ∧ r.

Let p, q and r be statements. Suppose you know that the statement form ((q → p) ∨ r) ∨ (∼ r ∧ p) is false. What can you conclude about the truth values of the three statement variables?

Model two contextualized problems using binary trees both quantitatively and qualitatively

Prove the following sentences using any prove method [ the most appropriate one]: a) If r is rational and s is irrational, prove that 2r+s is irrational. b) If t and s are integers and t × s is even, then t is even or s is even.

Prove that (a ∧ (b → ¬a)) → ¬b is a tautology.

Prove that the following argument is valid. Write all the necessary steps a)Rashid didn’t perform well in the subject, but he was present in every class. b)Every student who completed all the assignments, performed well in the subje…

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

The trivial negation of a proposition is: “It is not the case that [proposition]." Write two negations of the following, one trivial and one not trivial. (a) It is snowing. (b) At least 3 inches of snow fell yesterday. (c) 1…

Let P (x,y) denote the sentence 2x+y=5. what are truth value of the following domain of x and y is the set of all integers?

Sketch the Venn diagrams for each of these combinations of the sets A,B,C. (A ∪ B) ∩ C

a) A study was conducted on some 400 employees of a certain company to establish the favorite beverage from among Coffee, Tea and Cocoa. The following was observed: 145 employees preferred Coffee, 165 preferred Tea while 185 prefe…

A Survey of 118 persons was conducted at TCC, and it was found at 24 persons carried a cell phone, 59 persons carried a tablet computer and 12 carried both a cell phone and a tablet. how many people carried a cell phone or a tablet? …

What do universal set, S, have 91 elements. A and B are subsets of S. Set a contains 20 elements and CB contains 44 elements. If sets A and B have 6 elements in common, how many elements are in A but not in B?

Let A = {a,b,d,e,g,f,1,2,3}, B = {1,2,3}, and C = {1,2,3,a,d,g}. Find the following: (i) A ՈB Ս C (ii) A-B (iii) (B Ո C) x (A Ո C) (iv) P(B Ո C) (v) |CxA|

(a) Let A = {0,1, 2, 3, 4, 5}, B = {1, 2, 3, 4, 5, 6}, and consider the relation R = {(a, b) э A x B | a2+b2 < 30}. (i) List all the elements of the relation R and give its cardinality |R|. (3 marks) (ii) Find the domain and range …

(b) Let A = {5, 6, 7, 8}, B = { 4, 6, 7} and the relations R1 = {(a, b) | a эA, bэB and a > b} R2 = {(a, b) | a э A, b э B and (a – b)2 <=6} (i) Find the sets of ordered pairs in R1, R2 and give their cardinalities |R1|, |R2|. (2 m…

5a) Explain whether each of the following relations on the set of real numbers is a function or not. For those (if any) that are indeed functions say whether they are one-to-one and/or onto. (2 marks) i) y = f(x) = 2x2+1 xэR, y эR i…

Question 6 (6 marks) 6a) Draw the Venn diagrams for each of these combinations of the sets A, B, and C: (i) (A – C)C ⋂ ( B- C)C (3 marks) (ii) (A – C) U (C – B)(3 marks) End

Find a formula for 1+1+⋯+ 1 1 ⋅ 2 2 ⋅ 3 n(n + 1) by examining the values of this expression for small values of n. b) Prove the formula you conjectured in part

Prove that 12 +32 +52 +⋯+(2n+1)2 = (n+1)(2n+1)(2n + 3)∕3 whenever n is a non negative integer.

1. Is the function 𝑓: ℤ → ℤ 𝑓(𝑥) = 𝑥 2 + 3 injective, surjective or bijective? Prove your assertions

1. Show if satisfy the algebraic axioms: identity and inverse under addition. 2. Show if satisfy all (communicative, associative, identity, and inverse) the algebraic axioms under both multiplication and addition. 3.…

3a²n−1

find 200 sum k=100^k

Check whether the compound proposition (p ∨￢q) ∧(q ∨￢r) ∧(r ∨￢p) ∧(p ∨q ∨r) ∧(￢p ∨￢q ∨￢r) is satisfiable or not?

Given a function f from {1, 2,...,n}to the set of integers, determine whether f is one-to-one.

Why is f not a function from R to R if a) f (x) = 1/x? b) f (x) =√x? c) f (x) = ±√(x^2+1)?

BSIT section 1T is composed of 11 male students and 19 female students, how many choices do you have if there will be one (female) muse and one (male) escort

Mary’s Online Shop sells clothes for plus size women. It has 4 kinds of formal blazers, 7 kinds of inner blouses, and 9 kinds of designer jeans. Find the number of ways a person can buy an item

Determine the truth value of each of the following statements:/5mrks (i) Paris is in France or 4+4=8 (ii) 4+4=9 and5+8=11 (iii) m+2is the unit of area or Kg is the unit of mass (iv) If Kigali is capital city of Rwanda and Kampal…

1 + 1 =

¬𝑝 ∧ (𝑝 ∨ 𝑞)] ⇒ 𝑞

Given a set of five distinct science books, three distinct math books and two distinct history books. a. In how many ways can these books be arranged on a shelf?

Establish the validity of the argument with the premises p -> (q -> r) , p \/ s , t ->q , ~s and ~r -> ~t

Let Q(x) be the statement “x + 1 > 2x.” If the domain consists of all integers, what are these truth values? a) Q(0) b) Q(−1) c) Q(1) d) ∃xQ(x) e) ∀xQ(x) f) ∃x¬Q(x) g) ∀x¬Q(x)

A 1 team1 of :ll.1 players is so be chosen from 15 1 members. 11 n how ways rcan this, be done If I.. One pairticular player is always incliuded.

∃𝑥 (𝑥 + 1 = 0 ∨ 𝑥 + 2 = 0) write the negation of the following

whether each of these functions is a bijection from R to R. f (x) = x 3 -1

A) The probability that a free-lancer gets an electric contract is 2/7 and that of his getting a plumbing contract is 3/5. If the probability of his getting at least one of the contracts is 5/7. What is the probability of his gettin…

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

Every function is a relation, but the converse is not true.”--True or false? Justify with an example.

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