**Assignment Task**

**Task**

**Question 1.**

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Get expert assistance in any academic field. All courses and programs covered.

Get Help Now!**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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