S.chand books solution class 6

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)\( \notin \){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 ?

\( = \)​ {1,2,3,4}

\( = \)​ {2,3,4,5,6}

\( = \)​ {3,4,5,6}

D \( = \)​ {a,b,c,d,e}

\( = \)​ {The vertices of a triangle}

\( = \)​ {p,q,r}

\( = \)​ {Months of a year}

\( = \)​ {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)

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

\( = \) {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) \( = \) {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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