CS-6201 - Discrete Structures oed answer key

Showing 81 to 100 of 106 total answers.

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Awesome StudentQuestion • Discrete Structures 2

In examining the algorithm of multiplying two numbers and displaying the output, what is the next step after declaring the 3 integers a,b,c

Answer

define the values of a and b

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Awesome StudentQuestion • Discrete Structures 2

Which rule states that if (k + 1) or more objects are placed into k boxes, then there is at least one box containing two or more of the objects?

Answer

pigeonhole principle

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Awesome StudentQuestion • Discrete Structures 2

A class consists of 12 women and 10 men. How many ways are there to form a committee of size six if the committee has equal numbers of women and men?

Answer

C(12,3) =C2=B7 C(10,3)

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Awesome StudentQuestion • Discrete Structures 2

Assume that you have an ordinary deck of 52 playing cards. How many possible 7-card poker hands are there that contain at least one face card (J, Q, K)?

Answer

C(52,7) - C(40,7)

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Awesome StudentQuestion • Discrete Structures 2

Consider the statement, "If n is divisible by 30 then n is divisible by 2 and by 3 and by 5." Which of the following statements is equivalent to this statement?

Answer

If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30

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Awesome StudentQuestion • Discrete Structures 2

One light bulb is selected at random from a lot of 110 light bulbs, of which 2% are defective. What is the probability that the light bulb selected is defective?

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Awesome StudentQuestion • Discrete Structures 2

What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 30 sec, the yellow signal for 5 sec, and the green signal for 40 sec?

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Awesome StudentQuestion • Discrete Structures 2

If you give a proof by mathematical induction of the statement that 2n &ge= n2, for all integers n =E2=89=A5 4, the basis step requires you to prove that which of the following is true?

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Awesome StudentQuestion • Discrete Structures 2

If two finite states machine M and N are isomorphic, thenA. M can be transformed to N, merely re-labelling its statesB. M can be transformed to N, merely re-labelling its edgesWhich is true?

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Awesome StudentQuestion • Discrete Structures 2

Suppose you want to prove that every product of integers of the form k(k+1)(k+2) is divisible by 6. If you want to prove this by cases, which of the following is a set of cases you would use?

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Awesome StudentQuestion • Discrete Structures 2

You have 12 balls, numbered 1 through 12, which you want to place into 4 boxes, numbered 1 through 4. If boxes can remain empty, in how many ways can the 12 balls be disturbed among the 4 boxes?

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Awesome StudentQuestion • Discrete Structures 2

Suppose you want to use the principle of mathematical induction to prove that 1 + 2 + 22 + 23 + 23 + ... + 2n = + 2n+1 - 1 for all non-negative integers n. Which of theses is the correct statement P(k) in the inductive step?

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Awesome StudentQuestion • Discrete Structures 2

Suppose you want to use the principle of mathematical induction to prove that 1 + 2 + 22 + 23 + 23 + ... + 2n = + 2n+1 - 1 for all positive integers n. Which of these is the correct implication p(k) -> P(k+1) to be used in the inductive step?

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Awesome StudentQuestion • Discrete Structures 2

How many different license plates are available if the license plate pattern consists of four letters that cannot be repeated and followed by three digits that can be repeated? (Assume that all letters are uppercase and the digits are 0, 1, ... 9)

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Awesome StudentQuestion • Discrete Structures 2

Suppose you are hired by a company at an initial salary of $30,000. At the end of each year you receive a 3% raise, plus an addition of $1000 on your base salary. Let an equal your salary at the end of n years with the company. Find a recurrence relation for an.

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Awesome StudentQuestion • Discrete Structures 2

The number of cars entering a tunnel leading to an airport in a major city over a period of 200 peak hours was observed and the following data were obtained: Cars, xFrequency of Occurrence152040654515Find the empirical probability distribution for this experiment.

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Awesome StudentQuestion • Discrete Structures 2

How many different passwords are possible if each password consists of six characters where each character is either an uppercase letter, a lowercase letter, or a digit, and at least one digit must be included in the password? (Note: There are 26 letters and 10 digits)

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Awesome StudentQuestion • Discrete Structures 2

A binary tree of depth "d" is an almost complete binary tree if. A. Each leaf in the tree is either at level "d" or at level "d- 1" B. For any node "n" in the tree with a right descendant at level "d" all the left descendants of "n" that are leaves, are also at level "d"

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Awesome StudentQuestion • Discrete Structures 2

How many different choices of winners can you have if the draw is limited to first year and second year students and you only have one grand prize? Note: Given that the population of the school is as follows: 1st year = 100 students, 2nd year = 98 students, 3rd year = 102 students, 4th year = 50 students.

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CS-6201 - Discrete Structures oed answer key

In examining the algorithm of multiplying two numbers and displaying the output, what is the next step after declaring the 3 integers a,b,c

Which rule states that if (k + 1) or more objects are placed into k boxes, then there is at least one box containing two or more of the objects?

A class consists of 12 women and 10 men. How many ways are there to form a committee of size six if the committee has equal numbers of women and men?

Assume that you have an ordinary deck of 52 playing cards. How many possible 7-card poker hands are there that contain at least one face card (J, Q, K)?

Consider the statement, "If n is divisible by 30 then n is divisible by 2 and by 3 and by 5." Which of the following statements is equivalent to this statement?

One light bulb is selected at random from a lot of 110 light bulbs, of which 2% are defective. What is the probability that the light bulb selected is defective?

What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 30 sec, the yellow signal for 5 sec, and the green signal for 40 sec?

If you give a proof by mathematical induction of the statement that 2n &ge= n2, for all integers n =E2=89=A5 4, the basis step requires you to prove that which of the following is true?

If two finite states machine M and N are isomorphic, thenA. M can be transformed to N, merely re-labelling its statesB. M can be transformed to N, merely re-labelling its edgesWhich is true?

Suppose you want to prove that every product of integers of the form k(k+1)(k+2) is divisible by 6. If you want to prove this by cases, which of the following is a set of cases you would use?

You have 12 balls, numbered 1 through 12, which you want to place into 4 boxes, numbered 1 through 4. If boxes can remain empty, in how many ways can the 12 balls be disturbed among the 4 boxes?

Suppose you want to use the principle of mathematical induction to prove that 1 + 2 + 22 + 23 + 23 + ... + 2n = + 2n+1 - 1 for all non-negative integers n. Which of theses is the correct statement P(k) in the inductive step?

Suppose you want to use the principle of mathematical induction to prove that 1 + 2 + 22 + 23 + 23 + ... + 2n = + 2n+1 - 1 for all positive integers n. Which of these is the correct implication p(k) -> P(k+1) to be used in the inductive step?

How many different license plates are available if the license plate pattern consists of four letters that cannot be repeated and followed by three digits that can be repeated? (Assume that all letters are uppercase and the digits are 0, 1, ... 9)

Suppose you are hired by a company at an initial salary of $30,000. At the end of each year you receive a 3% raise, plus an addition of $1000 on your base salary. Let an equal your salary at the end of n years with the company. Find a recurrence relation for an.

The number of cars entering a tunnel leading to an airport in a major city over a period of 200 peak hours was observed and the following data were obtained: Cars, xFrequency of Occurrence152040654515Find the empirical probability distribution for this experiment.

How many different passwords are possible if each password consists of six characters where each character is either an uppercase letter, a lowercase letter, or a digit, and at least one digit must be included in the password? (Note: There are 26 letters and 10 digits)

A binary tree of depth "d" is an almost complete binary tree if. A. Each leaf in the tree is either at level "d" or at level "d- 1" B. For any node "n" in the tree with a right descendant at level "d" all the left descendants of "n" that are leaves, are also at level "d"

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