Computational Mathmatics

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 1 of 3

ITSU2011

Computational Mathematics

Activity 05

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) Rewrite in set notation:

i. All squares are rectangles.

ii. Not all rectangles are rhombuses.

Q2) Rewrite in an English sentence using the words ‘all’ or ‘not all’:

i. {whole number multiples of 6} ⊆ {even whole numbers}.

ii. {square whole numbers} ⊆ {even whole numbers}.

Q3) Rewrite the statements in part (b) in an English sentence using the words ‘if …, then’.

Q4) Given the sets A = {0, 1, 4, 5} and B = {1, 4}:

i. Draw a Venn diagram of A and B using the universal set U = {0, 1, 2, …, 8}.

ii. Graph A on the number line.

Q5) Let the universal set be E = {whole numbers less than 20}, and let

A = {squares less than 20}

B = {even numbers less than 20}

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

C = {odd squares less than 20}

i. Draw A and C on a Venn diagram, and place the numbers in the correct regions.

ii. Draw B and C on a Venn diagram, and place the numbers in the correct regions.

iii. cShade A ∩ B on a Venn diagram, and place the numbers in the correct regions.

iv. Shade A ∪ B on a Venn diagram, and place the numbers in the correct regions.

Q6) Twenty-four people go on holidays. If 15 go swimming, 12 go fishing, and 6 do neither,

how many go swimming and fishing? Draw a Venn diagram and fill in the number of people in

all four regions.

Q7) If U = {a,b,c,d,e}, A = { a,b,d} and B = {b,d,e}. Prove De Morgan's law of intersection.