Chapter 1

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 5. 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. - 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. - 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

- 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}

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