Computational Mathmatics

Victorian Institute of Technology Pty Ltd

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ITSU2011 – Computational Mathematics Page 1 of 3

ITSU2011

Computational Mathematics

Activity 01

Victorian Institute of Technology Pty Ltd

ABN: 41 085 128 525 RTO No: 20829 TEQSA ID: PRV14007 CRICOS Provider Code: 02044E

ITSU2011 – Computational Mathematics Page 2 of 3

Q1

Which of the following are propositions?

(a) Buy Premium Bonds!

(b) The Apple Macintosh is a 16-bit computer.

(c) There is a largest even number.

(d) Why are we here?

(e) 8 + 7 = 13

(f) a + b = 13

Q2

p is "1024 bytes is known as 1MB"

q is "A computer keyboard is an example of a data input device".

Express the following compound propositions as English sentences in as natural a way as you can. Are the resulting propositions true or false?

(a) p ˄ q

(b) p ∨ q

(c) ¬p

Q3

p is "x < 50"; q is "x > 40".

Write as simply as you can:

(a) ¬p

(b) ¬q

(c) p ˄ q

(d) p ∨ q

(e) ¬p ˄ q

(f) ¬p ˄ ¬q

Q4

One of these compound propositional functions always produces the output true, and one always outputs false. Which ones?

p is "I like Maths"

q is "I am going to spend at least 6 hours a week on Maths"

Write in as simple English as you can:

(a) (¬p) ˄ q

(b) (¬p) ∨ q

(c) ¬(¬p)

(d) (¬p) ∨ (¬q)

(e) ¬(p ∨ q):

(f) (¬p) ˄ (¬q)

Q5

Victorian Institute of Technology Pty Ltd

ABN: 41 085 128 525 RTO No: 20829 TEQSA ID: PRV14007 CRICOS Provider Code: 02044E

ITSU2011 – Computational Mathematics Page 3 of 3

In each part of this question a proposition p is defined. Which of the statements that follow the definition correspond to the proposition ¬p? (There may be more than one correct answer.)

(a)

p is "Some people like Maths".

(i) "Some people dislike Maths"

(ii) "Everybody dislikes Maths"

(iii) "Everybody likes Maths"

(You may assume in this question that no-one remains neutral: they either like or dislike Maths.)

(b)

p is "The answer is either 2 or 3".

(i) "Neither 2 nor 3 is the answer"

(ii) "The answer is not 2 or it is not 3"

(iii) "The answer is not 2 and it is not 3"

(c)

p is "All people in my class are tall and thin".

(i) "Someone in my class is short and fat"

(ii) "No-one in my class is tall and thin"

(iii) "Someone in my class is short or fat"

(You may assume in this question that everyone may be categorised as either tall or short, either thin or fat.)

Q6

Construct truth tables for:

(a) ¬p ∨ ¬q

(b) q ˄ (¬p ∨ q)

(c) p ˄ (q ∨ r)

(d) (p ˄ q) ∨ r