The Corruption Perceptions Index uses perceptions of the general public, business people, and risk analysts to rate countries by how likely they are to accept bribes. The ratings are on a scale from 0 to 10, where higher scores represent less corruption. The graph shows the corruption ratings for the world’s least corrupt and most corrupt countries.

Consider the statement If the country is Finland, then the corruption rating is 9.6.

(i) Write each statement in symbolic form. Then use the information displayed by the graph below to determine the truth value of this conditional statement.

(ii) Write the converse, inverse, and contrapositive of the statement in part (i). Then use the information given by the graph to determine whether each statement is true or not necessarily true.

(b) Write each statement in symbolic form. Then use the information displayed by the graph below to determine the truth value of the compound statement

(i) Twenty-nine percent consider religion the most taboo topic and it is not true that 14% consider politics the most taboo topic.

(ii) If a greater percentage of people consider money a more taboo topic than personal life, then 16% consider money the most taboo topic and 14% consider personal life the most taboo topic.

(iii) Fourteen percent consider money the most taboo topic if and only if 14% consider polities the most taboo topic, or it is not true that the greatest percentage consider religion the most taboo topic.

QUESTION 2

An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The results were as follows: 894 drank alcohol regularly, 665 smoked cigarettes, 192 used illegal drugs, 424 drank alcohol regularly and smoked cigarettes,

114 drank alcohol regularly and used illegal drugs, 119 smoked cigarettes and used illegal drugs, 97 engaged in all three behaviors, and 309 engaged in none of these behaviors. Source: Jamie Langille, University of Nevada Las Vegas

(a) Construct a Venn diagram and determine the cardinality for each region.

(b) How many students were surveyed? (2 marks) Of those surveyed,

(c) How many drank alcohol regularly or smoked cigarettes? (2 marks)

(d) How many used illegal drugs only? (1 mark)

(e) How many drank alcohol regularly and smoked cigarettes, but did not use illegal drugs? (1 mark)

(f) How many drank alcohol regularly or used illegal drugs, but did not smoke cigarettes? (2 marks)

(g) How many engaged in exactly two of these behaviors? (2 marks)

(h) How many engaged in at least one of these behaviors? (2 marks)

QUESTION 3

List the ordered pairs in the relations R from A = {0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a, b) ∈ R if and only if

(a) a = b (1 mark)

(b) a + b = 4 (1 mark)

(c) a – b = 2 (1 mark)

(d) a > b (2 marks)

QUESTION 4

A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 70% of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. Assume that 70% of all people like this hamburger. On a certain day, ten customers bought it. Let X denote the number of customers in this sample of 10 who will like this hamburger.

(a) Using the appropriate probabilities table, obtain the probability distribution of X.

(b) Determine the mean and variance of X. (4 marks)

QUESTION 5

Two boxes each contain three cards. The first box contains cards labeled 1, 3 and 5; the second box contains cards labeled 2, 6 and 8. In

a game, a player draws one card at random from each box and his score, X, is the sum of the numbers on the two cards.

(a) Determine the probability distribution of X. (6 marks)

(b) Determine the probability of X takes even value and the probability of X = a multiple of 3. (4 marks)

(c) Calculate the mean and variance of X. (5 marks)

QUESTION 6

Description:

Write a report (at least 5 pages) based on the topic : Graph Theory

1.Introduction.

2. History.

3. Importance.

4. Application in real-life (at least 3 applications). Describe real-life examples of how to apply graph theory to model and solve problems in AI, data science and computer science.

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