**Exercise 1 (A)**

**1.Which of the following collection are sets ? If not a set , give reasons.**

**(a)** Planets in our solar system.

**(b)** Interesting books in the library.

**(c)** Colours of the Rainbow.

**(d)** All difficult problems in your maths book.

**(e)** Top five wicket takers in test cricket.

**(f)** Intelligent boys of your class.

**(g)** Presidents of India.

**(h)** Good football players.

**(i)** Counting numbers between 30 and 40.

**(j)** All good schools of India.

**(k)** All vowels.

**(l)** All yellow fruits.

**Exercise 1 (B)**

**1.State whether the following sentences are true or false.**

**(a)** b \( \notin \){a,e,i,o,u}

**(b) **6 \( \in \) the set of even numbers.

**(c) **13 \( \notin \) the set of odd numbers.

**(d) **Gold \( \notin \) {Silver,Platinum,Gold}.

**(e) **Geetanjali \( \notin \) the set of books written by Tagore.

**(f)** Rose \( \notin \) the set of all vegetables.

**(g)** 1998 \( \in \) the set of leap year.

**(h)** Moon \( \in \) the set of planets of the Solar System.

**2.Let A \( = \) {odd numbers \( \leq \)19 }.Insert the appropriate symbol ’\( \in \)’ or ’\( \notin \)’ in blank spaces.**

**(a)** 4 __ A

**(b)** 7 __ A

**(c)** 9 __ A

**(d)** 13 __ A

**(e)** 19 __ A

**(f)** 2 __ A

**3.Write three sentences in set language using the proper symbols ’\( \in \)’ or ’\( \notin \)’:**

**(a) **2 is a member of the set of first five counting numbers.

**(b) **d is the member of the set of consonants.

**(c) **32 is not a member of the set of multiples of 3.

**(d) **India is not a member of the set of continents.

**Exercise 1 (E)**

**1,State which of the following sets are finite and which are infinite :**

**(a)** {Numbers of peoples in India.}

**(b)** {Multiples of 7.}

**(c)** {0,1,2,3, ……. }

**(d)** {x \( | \) x is a multiple of 2 less than 48.}

**(e)** The set of teachers in your school.

**(f)** The set of animals on earth.

**(g)** The set of leaves on a tree.

**(h)** The set of grains of sand on the beach.

**(i)** The set of men who have landed on the moon.

**(j)** The set of atoms in the earth.

**2.Which of the following are singleton sets ?**

**(a)** {Capital of India.}

**(b) **{Mountain peaks more than 800 m high }

**(c) **{The men who have landed on moon.}

**(d) **{Even numbers which are prime.}

**3.State which of the following are null or empty sets ?**

**(a)** The set of women army chief in India since 1947.

**(b)** {Men over 300 year old.}

**(c)** The set of odd number divisible by 2.

**(d)** The set of teachers teaching you.

**(e)** {Cubes with 8 faces}

**(f)** {Days with 1440 minutes}

**(g)** {Even numbers which are prime.}

**(h)** { x \( | \) x is a person over 100 m tall }

**(i)** {Horses which have five legs.}

**(j)** {Capitals of the states of India.}

**Exercise 1 (F)**

**1.What is the cardinal number of each of the following sets ?**

**(a) **The set of hours in a day.

**(b) **The set of prime numbers less than.

**(c) **The set of inventions: telephone,pendulum, wheel , and computer.

**(d) **The set of scientists: Raman, Bhabha and Einstein.

**(e) **The set of months of the year with names that begin with the letter S.

**(f) **The set of weeks having 8 days.

**(g) **P \( = \) {planets in our solar system}

**(h) **K \( = \) {Letters in the word ‘MADAM’}

**(i) **C \( = \) {consonants of the English Alphabet}

**2.Which of the following sets are equivalent to each other ?**

**A **\( = \) {1,2,3,4}

**B **\( = \) {2,3,4,5,6}

**C **\( = \) {3,4,5,6}

**D** \( = \) {a,b,c,d,e}

**E **\( = \) {The vertices of a triangle}

**F **\( = \) {p,q,r}

**G **\( = \) {Months of a year}

**H **\( = \) {natural numbers from 1 to 12}

**3.Which of the following pairs of sets are equal sets ?**

**(a)** P \( = \) {a,b,c,d} , Q \( = \) {d,a,c,b}.

**(b)** A \( = \) {Anil,Suresh,Prem,Hari} , B \( = \) {Prem,Anil,Hari,Suresh}

**(c)** M \( = \) {r,e,d} , N \( = \) {d,a,r}

**(d)** X \( = \) {0,1,2,3} , Y \( = \) {Whole number less than 4}

**(e)**

A \( = \) {students in your class who are more than 50 years old},

B \( = \) {months of the year whose name begin with R}

**(f)** R \( = \) {Set of all girl’s names beginning with J} , S \( = \) {Joan, Jean , Judy , Julie}

**(g)** A \( = \) Set of all whole numbers between \( \dfrac{3}{4} \) and \( \dfrac{25}{3} \) , B \( = \) {2,3,4,5,6,7,8}

**(h)**

(i) The set J of whole numbers from 1 to 6 inclusive.

(ii) The set K \( = \) {0,1,2,3,4,5}

(iii) The set L of the number of faces of a die.

**4.Write T or F to show whether the statements is true or false.**

**(a) **All examples of the empty sets are equal.

**(b) **All examples of the empty sets are equivalent.

**(c) **If two sets are equal, they are equivalent.

**(d) **If two sets are equivalent, they are equal.

**Exercise 1 (G)**

**1.From the following pairs of sets, identify the disjoint and overlapping sets :**

**(a) **A \( = \) set of letters in the word ‘MAD’ , B \( = \) set of letters in word ‘PEN’

**(b)** P \( = \) set of the digits in the number ‘3150’ , Q \( = \) sets of the digits i the number ‘2468’

**(c)** E \( = \) set of months having 30 days. , F \( = \) set of months having 31 days.

**(d)** A \( = \) {multiples of 3 between 9 and 45} , B \( = \) {multiples of 4 between 8 and 40}

**(e)** P \( = \) {whole numbers between 25 and 100} , Q \( = \) {whole numbers between 60 and 150}

**(f)** R \( = \) {letters in the words ‘AMERICA’} , S \( = \) {letters in the word ‘INDIA’}

**2.List the members of the following sets.**

**(a)** {4,5,6,7} \( \cup \) {8,9,10,11}

**(b)** {gold , silver} \( \cup \) {iron,copper ,zinc,aluminium}

**(c)** {cat , horse,dolphin} \( \cup \) {whale,octopus}

**(d)** {0,1,3,5,7,8,10} \( \cup \) {2,6,7,14}

**(e)** {a,b,c,d,e,f} \( \cup \) {b,d,f,g,h}

**3.Set X,W,Y and Z are described below.**

W \( = \) the set of all pets,

X \( = \) the set of all dogs,

Y \( = \) the set of all rabbits,

Z \( = \) the set of all four legged animals.

**Find**

(i) Z \( \cup \) X

(ii) W \( \cup \) Y

(iii) Z \( \cup \) Y

(iv) W \( \cup \) X

(v) Y \( \cup \) X

4.Suppose A is the set of letters in ‘SONG’ and B is the set of letters in ‘SORRY’,what is A \( \cup \) B.

**Exercise 1 (H)**

**1**.Let A \( = \) set of letters in ‘NIGHT’ and B \( = \) set of letters in ‘NET’,find A \( \cap \) B.Are these overlapping set?

**2**.Suppose S is the set of letters in BOY and T is the set of letters in GIRL.What is S \( \cap \) T ? Are they disjoint sets?

**3**. Let A \( = \) {0,1,5,9}, B \( = \) {5,7,9,11}.Are they overlapping sets?What is A \(\cap \) B ?

**4**.Let P \( = \) {a,b,c}, Q \( = \) {d,e,f}. Are they disjoint sets? What is P \(\cap \) Q.

**5**.Suppose A is the set of letters in the word FOOTBALL and B is the set of letters in the word SPORT.What is A \(\cap \) B ?

**6.**Let P \( = \) {a,b,c,d,e,f} , Q \( = \) {a,b} , R \( = \) {b,c,d,e} , S \( = \) {d,e,f} and T \( = \) {f,g,h} , find :

**(i)** P \(\cap \) Q

**(ii)** Q \(\cap \) R

**(iii)** P \(\cap \) R

**(iv)** S \(\cap \) R

**(v)** P \(\cap \) T

**(vi)** Q \(\cap \) T

**(vii)** P \(\cap \) S

**(viii)** R \(\cap \) T

**(ix)** S \(\cap \) T

**(x)** Q \(\cap \) S

**8.**What is the intersection of the set of odd numbers and set of whole numbers ?

**9.**Let A \( = \) {1,3,5,7}, B \( = \) {0,1,2,4,8}, C \( = \) {3,5,6} , D \( = \) {6,7,8,10} and E \( = \) {0}.Find:

**(i) **A \(\cap \) B

**(ii) **(A \(\cup \) B ) \(\cap \) D

**(iii) **B \(\cap \) E

**(iv) **(B \(\cup \) E)\(\cap \) D

**10.**

Let S \( = \) {non – zero multiples of 3 less than 20},

T \( = \) {non – zero multiples of 6 less than 20}.Find S \(\cap \) T

Tell whether S and T are disjoint sets or overlapping sets.

**Exercise 1 (I)**

**1.**Represent the following sets by Venn-diagrams:

**(i) ** A \( = \) {odd numbers less than 10}

(ii) P \( = \) {Multiples of 4 less than 40}

(iii) C \( = \) {letters in the word ‘MATHEMATICS’}

(iv) B \( = \) {x \( | \) x is a prime number less than 20}

(v) Q \( = \) {consonants in the word ‘INDIA’}

**2.Illustrate the given information about each pair of sets on a Venn-diagram. Also show the union and intersection of each pair by suitable Venn diagrams.**

(i) A \( = \)

(ii) P \( = \)

(iii) C \( = \)

(iv) E \( = \)

(v) A \( = \)

(vi) P\( = \)

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