Discrete OED Prelim-Finals PDF

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It is a rule that assigns each input exactly one outputAnswer: functionQuestion 2Correct Mark 1 out of 1.Flag question Question textDetermine whether the sentence below is an atomic statement, a molecular statement, ornot a statement at all. The customers wore shoes. Atomic Feedback Your answer is c...

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It is a rule that assigns each input exactly one output Answer:

function

Question 2 Correct Mark 1.00 out of 1.00

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Question text Determine whether the sentence below is an atomic statement, a molecular statement, or not a statement at all. •

The customers wore shoes.

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Question text Assume the sequence: 1,3,5,7,9, …. What is the 20th term?

29

What type of progression this suggest?

Arithmetic

Atomic

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Question text Match the truth tables to its corresponding propositional logic

Answer 1

Answer 2

Answer 3

Implication

Disjunction

Conjunction

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Question text

Proofs that is used when statements cannot be rephrased as implications. Answer:

proof of contradiction

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Question text ¬P ∨ Q is equivalent to : Select one: a. P→Q b. ¬P ∧ ¬Q c. ¬(P∨Q)

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Question text In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One is a square, and the other is a triangle. Each shape is drawn in a single color. Suppose you believe me when I tell you that if the square is blue, then the triangle is green. What do you therefore know about the truth value of the following statements? Select one: a.

The square is not blue or the triangle is green. b. If the triangle is not green, then the square is not blue. c. The square and the triangle are both green. d. If the triangle is green, then the square is blue. e. The square and triangle are both blue.

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Question text A sequence that involves a common difference in identifying the succeeding terms. Select one: a. Arithmetic Progression b. Geometric Progression

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Question text How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? Answer:

720

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Question text Given the series : 2,5,8,11.... What is the type of progression? Arithmetic What is the sum from 1st to 5th element? 40 14 Geometric

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Question text Which of the following statements are equivalent to the implication, “if you win the lottery, then you will be rich,”? Select one or more: a. You will win the lottery if you are rich. b. Either you don’t win the lottery or else you are rich. c.

If you are rich, you must have won the lottery. d. You will be rich only if you win the lottery. e. It is sufficient to win the lottery to be rich. f. Either you win the lottery or else you are not rich. g. You will win the lottery and be rich. h. Unless you win the lottery, you won’t be rich. i. You will be rich if you win the lottery. j. It is necessary for you to win the lottery to be rich.

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Question text Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? Select one: a. 210 b.

21100 c. 2100 d. 244000

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Question text What is the matching number for the following graph?

Answer:

4

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Question text If n is a rational number, 1/n does not equal n-1.

Select one: True False Question 15 Correct

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Question text Find the cardinality of S = {1, {2,3,4},0} | S | = Answer

3

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Question text Let ‘G’ be a connected planar graph with 20 vertices and the degree of each vertex is 3. Find the number of regions in the graph. Answer:

12

Feedback Solution By the sum of degrees theorem, 20 ∑ i=1 deg(Vi) = 2|E| 20(3) = 2|E| |E| = 30 By Euler’s formula, |V| + |R| = |E| + 2 20+ |R| = 30 + 2 |R| = 12 Hence, the number of regions is 12.

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Question text Determine whether the sentence below is an atomic statement, a molecular statement, or not a statement at all. •

The customers wore shoes and they wore socks.

Molecular

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Question text Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7} Find A ∩ B Select one: {1, 2, 6, 7}

{5, 6, 7} {3, 4, 5} {1, 2, 3}

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Question text Determine whether the sentence below is an atomic statement, a molecular statement, or not a statement at all. Not a statement at all

(a) Customers must wear shoes. (b) The customers wore shoes.

Atomic statement

(c) The customers wore shoes and they wore socks.

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Question text

Molecular statement

In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One is a square, and the other is a triangle. Each shape is drawn in a single color. Suppose you believe me when I tell you that if the square is blue, then the triangle is green. What do you therefore know about the truth value of the following statement? The square and the triangle are both green.

The statement is FALSE

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Answer the following: f (1) =

4

What is the element n in the domain such as f Find an element n of the domain such that f

= n.

3

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=1

2

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Question text Suppose P and Q are the statements: P: Jack passed math. Q: Jill passed math. Which of the following translates into “Jack and Jill both passed math” into symbols? Select one: a. PνQ b. PΛQ c. P→Q d. ¬(P Λ Q)

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Question text Consider the statement, “If you will give me a cow, then I will give you magic beans.” Determine whether the statement below is the converse, the contrapositive, or neither.

•

If I will give you magic beans, then you will give me a cow.

Converse

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Question text In my safe is a sheet of paper with two shapes drawn on it in colored crayon. One is a square, and the other is a triangle. Each shape is drawn in a single color. Suppose you believe me when I tell you that if the square is blue, then the triangle is green. What do you therefore know about the truth value of the following statement? The square and the triangle are both blue.

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The statement is FALSE

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Question text inverse image

• The Answer B}.

of a a subset B of the codomain is the set f −1 (B) {x ∈ X : f (x) ∈

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Question text Rule that states that every function can be described in four ways: algebraically (a formula), numerically (a table), graphically, or in words. Select one: a. Rule of thumb b. Rule of four c. Rule of function

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Find the contrapositive of the given statement. If you travel to London by train, then the journey takes at least two hours. Select one: a. If your journey by train takes less than two hours, then you don’t travel to London. b. If your journey by train takes more than two hours, then you don't travel to London.

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Answer the following: f (1) =

4

What is the element n in the domain such as f Find an element n of the domain such that f

= n.

3

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=1

2

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Question text The ________________________ states that if event A can occur in m ways, and event B can occur in n disjoint ways, then the event “A or B” can occur in m + n ways. Select one: a. Commutative principle b. Additive principle c. Distributive principle

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Question text bijection

A Answer is a function which is both an injection and surjection. In other words, if every element of the codomain is the image of exactly one element from the domain

A function which renames the vertices. Select one: a. non-isomorphism b. isomorphism

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Question text Consider the statement, “If you will give me a cow, then I will give you magic beans.” Determine whether the statement below is the converse, the contrapositive, or neither. •

If I will give you magic beans, then you will give me a cow.

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Contrapositive

Question text Consider the statement, “If you will give me a cow, then I will give you magic beans.” Determine whether the statement below is the converse, the contrapositive, or neither. •

If you will give me a cow, then I will not give you magic beans.

Converse

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Question text Classify the sentence below as an atomic statement, a molecular statement, or not a statement at all. If the statement is molecular, identify what kind it is (conjuction, disjunction, conditional, biconditional, negation). The Broncos will win the Super Bowl or I’ll eat my hat. Molecular

Conjunction

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Question text

Does a rational r value for r2 =6 exist? Select one: a. No, a rational r does not exist. b. Yes, a rational r exist.

Feedback Your answer is correct. r2 = 6 r = √(6) The number 6 is not a perfect square. Also, the square root of 6 cannot be written as a simple fraction because there many significant non-repeating digits after the decimal point.

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Question text Let A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, and C = {2, 3, 5}. Find A ∩ (B U C)

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Question text If the right angled triangle t, with sides of length a and b and hypotenuse of length c, has area equal to c2/4, what kind of triangle is this?

Select one: a. scalene triangle b. isosceles triangle c. obtuse triangle

Feedback Your answer is correct. (a2+b2)/4=(1/2)ab Multiply both sides by 4 to get: a2+b2=2ab

Solving for 0 we get: a2-2ab+b2=0 And factoring the polynomial we get: (a-b)2=0 Take the square root of both sides: ±(a-b)=0 a=b Therefore, a triangle with two equal sides is an ISOSCELES Triangle.

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Question text De Morgan's law is used in finding the equivalence of a logic expression using other logical functions. Select one: True False Question 9 Correct Mark 1.00 out of 1.00

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Question text What is the matching number for the following graph?

Answer:

4

Feedback

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Question text Deduction rule is an argument that is not always right. Select one: True False Question 11 Correct Mark 1.00 out of 1.00

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Question text

Given the diagram, answer the following questions : How many people takes tea and wine? 32 How many people takes coffee but not tea and wine? 45 What is the difference of persons who take wine and coffee to the persons who the persons who takes tea only? 15 24

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Question text How many possible output will be produced in a proposition of three statements? Answer:

16

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Question text Identify the propositional logic of the truth table given

Select one: a. implication b. negation c. disjunction d. conjunction

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Question text A graph for which it is possible to divide the vertices into two disjoint sets such that there are no edges between any two vertices in the same set. Answer:

Bipartite graph

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Question text Find | R | when R = {2, 4, 6,..., 180} Answer:

178

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Question text For a function f : N → N, a recurrence definition consists of an initial condition together with a recurrence relation . recursive

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Question text Classify the sentence below as an atomic statement, a molecular statement, or not a statement at all. If the statement is molecular, identify what kind it is (conjuction, disjunction, conditional, biconditional, negation).

Everybody needs somebody sometime. Atomic

N/A

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Question text Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7} Find A \ B

Select one: {1, 2, 6, 7} {3, 4, 5} {1, 2, 3, 4, 5, 6, 7} {1, 2}

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Question text A graph is complete if there is a path from any vertex to any other vertex. Select one: True False Question 20 Correct Mark 1.00 out of 1.00

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Question text A set of statements, one of which is called the conclusion and the rest of which are called premises. Answer:

argument

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Question text ¬(P ∨ Q) is logically equal to which of the following expressions? Select one: a. ¬P ∧ ¬Q. b.

¬P ∨ Q c. ¬P ∨ ¬Q

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Question text Classify the sentence below as an atomic statement, a molecular statement, or not a statement at all. If the statement is molecular, identify what kind it is (conjuction, disjunction, conditional, biconditional, negation). Every natural number greater than 1 is either prime or composite. Atomic

Disjunction

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Question text Classify each of the sentences below as an atomic statement, a molecular statement, or not a statement at all. If the statement is molecular, say what kind it is (conjuction, disjunction, conditional, biconditional, negation).

(a) The sum of the first 100 odd positive integers. Not a statement

N/A

(b) Everybody needs somebody sometime. Atomic

N/A

(c) The Broncos will win the Super Bowl or I’ll eat my hat. Molecular

Conditional

(d) We can have donuts for dinner, but only if it rains. Molecular

Conditional

(e) Every natural number greater than 1 is either prime or composite. Atomic

Disjunction

(f) This sentence is false. Not a statement

N/A

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Question text How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? Answer:

720

Question 25

Incorrect Mark 0.00 out of 1.00

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Question text What is the minimum height height of a full binary tree?

Answer:

0

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Question text Suppose P and Q are the statements: P: Jack passed math. Q: Jill passed math. Which of the following translates into “Jack and Jill both passed math” into symbols? Select one: a. PΛQ b. PνQ c. ¬(P Λ Q) d. P→Q

Feedback

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Question text Arithmetic progression is the sum of the terms of the arithmetic series. Select one: True False Question 28 Correct Mark 1.00 out of 1.00

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Question text What is the 4th and 8th element of a Select one: a. 64,16 b. 16,64 c. 8,16 d. 32,64

Feedback Your answer is correct.

= n^(2) ?

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Question text Which of the following statements are equivalent to the implication, “if you win the lottery, then you will be rich,”? Select one or more: a. Either you don’t win the lottery or else you are rich. b. Either you win the lottery or else you are not...