Sets and Functions
Exercise 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.
- 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}
- A = {x/x2 + x – 6 } and B = { -3,2}. Is A = B?
- 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?
- 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}
- 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
- 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
- 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)
- 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
- 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
