Basic Techniques of Counting and Algorithm - Mathematics Assignment Help

Assignment Task

Task

Question 1.

a) Determine the contrapositive of this statement:

“Only if Marc studies will he pass the test”.

b) Using letters L, W, C for the component statements, translate the following compound statements into symbolic notation.

L (x): x is a lawyer
W (x) : x is a woman
C (x) : x is a chemist

i) There are some women lawyers who are chemists.    (2 marks)
ii) No woman is both a lawyer and a chemist.

c) Write each statement in symbolic form using p, q and r.

Question 2.
A fair six-sided dice is thrown and the scores are noted. Event X: The total of the two scores is 4.Even Y: The first score is 2 or 5.

a) Construct the table by showing the sample spaces.    (5 marks)
b) Find the probability of X and Y.    (3 marks)
c) Are events X and Y independent

Question 3.

Answer the following questions.

a) Freddie has 6 toys cars and 3 toy buses, all different.

i) He chooses 4 toys to take on holiday with him. In how many different ways can Freddie choose 4 toys?
ii) Freddie arranges these 9 toys in a line. Find the number of possible arrangements

• If the buses are all next to each other.
• If there is a car at each end of the line and no buses are next to each other.

b) There are 2 purple cubes, 3 blue cubes, 2 red cubes, 4 orange cubes, 2 green cubes and 2 yellow cubes. Calculate the number of possible arrangements when all the cubes are arranged in a line.

Question 4.

There were 100 students in the library who responded to how they completed their research paper.

• 18 students only used the periodicals.
• 29 students used the web and books.
• 15 students used books, the web, and periodicals.
• 40 students used books and periodicals.
• 20 used the web and periodicals.
• 60 students used books.
• 7 students did not use the web, nor books, nor the periodicals.

a) Represent this information with a Venn diagram.    (8 marks)
b) How many students only used the web in their research?    (2 marks)
c) How many students used books or periodicals?    (3 marks)

Question 5.

For the graph shown, determine if a semi-Eulerian, a Euler circuit, or neither. If yes, state the path.

Question 6.

Draw a binary search tree by inserting the values 50, 76, 21, 4, 32, 64, 15, 52, 14, 100, 83, 2, 3 and 70.

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