hmwelei

Sets and Functions
Exercise 1.1

1. Write each of the following sets (i) in set builder form (ii) in listing its elements.
   (1) The set N of natural numbers.
   (2) The set J of all positive integers.
   (3) The set P of all prime numbers.
   (4) The set A of all positive integers that lie between 1 and 13.
   (5) The set B of real numbers which satisfy the equation 3x2 + 5x – 2 = 0.
2. Choose a suitable description (a) of (b) or (c) in set builder form for the following sets.
   (1) E ={ 2, 4, 6, 8}
   (a) E = { x/ x is an even integer less than 10 }
   (b) E = { x/ x is an even positive integer less than 10 }
   (c) E = { x / x is positive integer, x< 10 and x is a multiple of 2}
   (2) F = { 3, 6,9, 12, 15 , …}
   (a) F = {x/ x is appositive integer that is divisible by 3}
   (b) F = {x/x is a multiple of 3}
   (c) F = {x/x is a natural number that is divisible by 3}
3. A = {x/x2 + x – 6 } and B = { -3,2}. Is A = B?
4. A = {x/x is prime number which is less than 10} and B = {x/x2 – 8x + 15 = 0}
   (a) Is A = B (b) Is B⊂ A?
5. P = {x/x is an integer and -1 < x<3/5 }and Q = {x/x3 -3x2 + 2x = 0} . Is P = Q?
   6.L= {(x,y)/ x and y are positive integers and x + y = 7}.Write L by listing its elements.

Exercise 1.2
1.Draw the following intervals.
(a) {x/x > 2} (b) {x/x ≥ 3} (c) {x/x x ≤ -1} (d) {x/x>-1}
(e){x/-2≤ x≤ 2} (f) {x/0≤x≤ 5} (g) {x/x≤0 or x.2}

1. Draw a graph to show the solution set of each of the following.
   (a) x-1<4 (b) x-1≤ 0 (c) 2x≤5 (d) 2x-1>7
   (e) 5-x≥1 (f) 1/3(x-1)<1
   3.Draw the graph of the following number lines below one another.
   (a) P = {x/x≥3, x∈R} (b) Q = {x/x≤-2, x∈R}
   (c) P∩Q (d) P∪Q
2. On separate number lines draw the graph.
   S = {x/x>-4} , T = {x/x<3}.Give a set –builder description of S∩T.

Exercise 1.3

1. M = {x/x is an integer , and -3<x<6} , N = the set of positive integers that are less than 8.
   Find M∩N. (3 marks)
2. A = {x/x is a positive integer that is divisible by 3}, B = {x/x is a positive integer that is
   divisible by 5. Find (a) A∩B B = { x/x is a prime number}. C = { x/x is a positive
   integer that is divisible by 3}. Find (a) A∩ (B∩C) and (A∩B) ∩C.
   Show that A∩ (B∩C)= (A ∩ B) ∩ C

1. Let A = {x/x is positive integer that is di