# Assignment on Types of Numbers

```Unit 2 Assignment 1 Intersections and Types of Numbers
1: Draw the venn diagram of the number system. Then place the following numbers in the correct position –1, 1, π, 7 , 3.333 3 ,
3
16
.
2: Let U = {–4, –
(a)
(c)
3:
2
33
, 1, π, 13, 26.7, 69, 10 }. A is set of integers in U. B is set of rational numbers in U.
3
List all the prime numbers contained in U.
List all the members of B.
(a)
(b)
(d)
List all the members of A.
List all the members of the set A
 B.

4
Given w = 4.3 x 10-3 x = 2.6 &times; 10 and y = , which of the following statements about the nature of x, y and w
(i)
x
y
(ii)
w &lt; y (iii)
(iv) x + y 
(v)
y
1
&lt; x (vii) x  y 
w
(vi)
(vii) w + x

4: Explain why the number 2π must be irrational, given that π is irrational.
5: Complete the table below, showing which of the number sets these numbers belong to:
Natural
Whole
Integer
Rational
Irrational
Real
5
0.5
5
–5
5√3 ∗ 2√3
5√3 + 2√3
(4-√3)(4 + √3)
6√2 − 3√8
7: Name the groups that &frac34; belongs to
8: Name the groups that 3 doesn’t belong to
9: Let A = {Odd numbers from 1-99}. Find set B so that A  B = 
10: Consider a right triangle with legs a=5 and b=7 and hypotenuse of c. Determine if the following are true or false:
(a) a*b is a natural number
(b) a – c is a rational number
(c) c2 is an integer
(d) b2 – c2 is a whole number
11: Let A ε {A,B,C,D,E,F,G,H) Let B ε {5 Vowels of the alphabet}. Find the following:
(a) A U B
(b) A  B
12: A set of numbers is considered closed if the operation of the set with itself will yield only that set. For example, integers are
closed under multiplication because an integer * integer will always be an integer but not closed under division because 7/0 isn’t
an integer. Determine if the following are closed or not. Give an example if it is not closed.
(a) Natural numbers under subtraction