Please write your College ID and the course number (IS2001) clearly on the top of each sheet you submit. Remember that marks are awarded for method as well as correct answers. This homework is to be handed in at the lecture to be given on the 21/1/1999.

Question 1
Express the following propositions in symbolic form:
(i) Either it is raining and I do not have an umbrella or it is not raining.
(5 marks)
(ii) If it is not raining, then I cannot stay at home. (5 marks)

Question 2
Write out the truth tables for the following compound expressions:
(i) p ® ((Øq) Ùp)(5 marks)
(ii) [(p® q) Ùq] ® p (5 marks)

Question 3
Write the converse, inverse, contrapositive and negation of the following statement:
``If the two lines given are parallel, then they have the same slope.''
(20 marks)

Question 4
Test the validity of the following argument:
If Sandra finishes her work, then if it does not snow she will go to the basketball game. It does not snow. Therefore if Sandra finishes her work she will go to the basket ball game. (10 marks)

Question 5
The domain of discourse is the whole world.
Let D(x) = ``x is a dog'' and C(x) = ``x is a cat''.
Translate the following into English:
(i) "x  [C(x) ® (ØD(x))] (5 marks)
(ii) $x  [(ØD(x)) Ù(ØC(x))] (5 marks)

Question 6
Let P(x,y) = ``x > y''. Let Q(x,y) = ``x-y > 0''.
Use these to write the following in symbolic form:

Question 7
Let A = {2,3,5,7}, B = {2,3}, C = {2,3,8,9}, E = { 2,3,5,7,8,9}.
Are the following true or false?
(i) 5 Î B
(ii) {2} Î B
(iii) B Í C
(iv) A Ì C
(v) A Ì N (10 marks)

Question 8
Let the universal set be E = {1,2,3, {1,2},5,8 }.
Let A = {1,2,{1,2},8}, B = {3,5,8}, C = {1,2,3,5,8}.
Find:
(i) A ÈB
(ii) A ÇC
(iii) B Ç[`C]
(iv) (A Ç[`B]) ÈC
(v) [`(([`B] È[`C]))] (10 marks)

Question 9
Fifty students each with 75p, visited a computer games arcade where there are three different computer games on offer. Seventeen of the students played each of the three computer games and 37 of them played at least two of them. No student played any game more than once. Each game costs 25p to play and the total proceeds from the student visit were £ 24.25. How many students prefered to watch and played none of the games?
(10 marks)