msep

9MathQ01-3,5
Chapter 1
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
   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}
3. 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
4. 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) L.C.M of 3 and 5
3. J = {1,2,3,4,……} the set of positive integers and P = {x/x is a prime number} ,find J∩P.
   4.A = {x/x is a positive even integer }. 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 divisible by 2}. B = { x/x is a positive integer that is
   divisible by 3}. C = {x/x is appositive integer that is divisible by 5}. List the elements of the
   sets A, B, C. Find (a) A∩ (B∩C) and (b) (A∩B) ∩C. Show that A∩ (B∩C)= (A ∩ B) ∩ C
   6.Let A = {x/x is a positive integer less than 7} and B = {x/x is an integer land -3 ≤ x ≤4}.
   List the number of A and B, and then write down A ∪ B.
2. Let A = {x/x is an integer, 0<x<6} and B = {x/x is a positive integer less than 13 and x is
   a multiple of 3}. List the number of A and B, and find A ∪ B.
3. If P = {x/x2 + 2x -3} and Q = {x/x is an integer, -1 ≤ x ≤ 4}, find P ∩ Q and P ∪ Q.

Exercise 1.4

1. Find the set B\A and A\B in the following.
   (a) A = { 1,2,3,4,5,6} , B = { 3,5} (b) A = { p,q,r,s} , B = { x,y,z}
   (c) A = { 1,2,3} , B = { 1,2,3,4}
2. S = the set of natural numbers and T = the set of positive even numbers. Describe in words
   the complement of T.
3. Let S = {1,2,3,4,5,6,7,8,9} and A = { 1,2,3,4,5}, B = { 2,4,6,8}. Find (a) A^' (b) B^'
   (c) A^'∩B^' (d) A∪B (e) (A∪B)^' what can you say about A^'∩B^' and (A∪B)^'?
4. S = {1,2,3,4,5,6,7,8}, A = {1,2,3,5,7}, B = {1,3,5,7}, C = {2,4,6,8}
   (i) List the sets A^', B^'and C^'.
   (ii) State whether each of the following is true or false.
   (a) A∩A^'=∅ (b) A∪A^'=∅ (c) A⊂B (d) B⊂A