Mathematics Semester II Solutions Solutions for Class 7 Math Chapter 4 Sets are provided here with simple step-by-step explanations. These solutions for Sets are extremely popular among Class 7 students for Math Sets Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Semester II Solutions Book of Class 7 Math Chapter 4 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Semester II Solutions Solutions. All Mathematics Semester II Solutions Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

Question W1.1:

Write which is a set and which is not a set in the groups given below.

Counting numbers

Counting numbers is a set. It is because, counting numbers are well defined objects, for instance 1, 2, 3, … .

Question W1.2:

Write which is a set and which is not a set in the groups given below.

Good cricket players of your school

Goodness of a cricket players may vary from person to person.”

So, good cricket players are not well defined.

Thus, good cricket players of our school are not a set.

Question W1.3:

Write which is a set and which is not a set in the groups given below.

All negative whole numbers

All negative whole numbers is a set because negative whole numbers are well defined objects, for instance 1, 2, 3, ….

Question W1.4:

Write which is a set and which is not a set in the groups given below.

All intelligent students of mathematics

All intelligent students of mathematics are not a set because intelligence of a student varies from person to person. So, intelligent students of mathematics are not well defined.

Question O1:

What is a set?

A set is a collection of well defined objects or numbers. Every element of a set is called the set element.

Question O2:

Which are the two methods of writing sets?

The two methods of writing sets are roster method and rule method.

Question W1.5:

Write which is a set and which is not a set in the groups given below.

Digits used in base five system.

Collection of digits used in base five systems is a set because digits used in base five systems are well defined objects, for instance 0, 1, 2, 3 and 4.

Question W2:

Write suitable answers in the blanks.

 Rule Method Roster Method 1. ---------------- 1. O = {1, 3, 5, 7, 9} 2. {months in a year} 2. ---------------- 3. ---------------- 3. V = {a, e, i, o, u} 4. {numbers on the face of a clock} 4. ----------------

 Rule method Roster method 1. (odd numbers from 1 to 10) 1. O = {1, 3, 5, 7, 9} 2. (months in a year) 2. M= {January, February, March, April, May, June, July, August, September, October, November, December } 3. (vowels of English alphabet) 3. V = {a, e, i, o, u} 4. (numbers on the face of a clock) 4. N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Question O3:

What are equivalent sets?

The sets which have same number of elements are called equivalent sets.

Question W3.1:

Write the following sets in rule method.

K = {5, 10, 15, 20, 25 ………….}

K = {multiples of 5}

Question W3.2:

Write the following sets in rule method.

L = {summer season, rainy season, winter season}

L = {Seasons of the year}

Question W5.5:

State whether the following are ‘True’ or ‘False’

A set of population of the world is an example for a finite set.

True

Reason: Population of the world can be counted.

Question O1:

Mention the name of a Mathematician who showed the method of representing sets through diagrams.

British mathematician, John Venn in the 19th century showed the method of representing sets through diagrams. The diagram used in sets is called Venn Diagrams.

Question W1:

If Solve the following problems. Draw Venn diagrams for each of them. A = {2, 3, 4, 5, 6}

B = {2, 4, 6, 8, 10}

C = {3, 6, 7, 9}

(1) A B = {2, 3, 4, 5, 6} {2, 4, 6, 8, 10}

= {2, 4, 6}

And the Venn diagram is: (2) B C = {2, 4, 6, 8, 10} {3, 6, 7, 9}

= {6}

And the Venn diagram is: (3) A C = {2, 3, 4, 5, 6} {3, 6, 7, 9}

= {3, 6}

And the Venn diagram is: (4) (A B) C = {2, 4, 6} {3, 6, 7, 9} (From (1) A B = {2, 4, 6})

= {6}

And the Venn diagram is: (5) A (B C) = {2, 3, 4, 5, 6} {6} (From (2) B C = {6})

= {6}

And the Venn diagram is: Question W2:

If Solve the following problems and draw Venn diagrams for each of them. P = {a, b, c, d, e}

Q = {a, e, i, o, u}

R = {a, c, e, g, i}

(1) P Q = {a, b, c, d, e} {a, e, i, o, u}

= {a, e}

And the Venn diagram is: (2) Q R = {a, e, i, o, u} {a, c, e, g, i}

= {a, e, i}

And the Venn diagram is: (3) P R = {a, b, c, d, e} {a, c, e, g, i}

= {a, c, e}

And the Venn diagram is: (4) (P Q) R = {a, e} {a, c, e, g, i} (From (1) P Q = {a, e})

= {a, e}

And the Venn diagram is: (5) P (Q R) = {a, b, c, d, e} {a, e, i} (From (2) Q R= {a, e, i})

= {a, e}

And the Venn diagram is: Question W3:

If Solve the following problems and draw Venn diagrams for each of them. X = {2, 3, 4, 5, 6}

Y = {1, 7, 8}

Z = {1, 3, 5, 7, 9}

(1) X Y = {2, 3, 4, 5, 6} {1, 7, 8}

= {1, 2, 3, 4, 5, 6, 7, 8}

And the Venn diagram is: (2) Y Z = {1, 7, 8} {1, 3, 5, 7, 9}

= {1, 3, 5, 7, 8, 9}

And the Venn diagram is: (3) X Z = {2, 3, 4, 5, 6} {1, 3, 5, 7, 9}

= {1, 2, 3, 4, 5, 6, 7, 9}

And the Venn diagram is: (4) (X Y) Z = {1, 2, 3, 4, 5, 6, 7, 8} {1, 3, 5, 7, 9}

(From (1) X Y = {1, 2, 3, 4, 5, 6, 7, 8} )

= {1, 2, 3, 4, 5, 6, 7, 8, 9}

And the Venn diagram is: (5) X (Y Z) = {2, 3, 4, 5, 6} {1, 3, 5, 7, 8, 9}

(From (2) Y Z = {1, 3, 5, 7, 8, 9})

= {1, 2, 3, 4, 5, 6, 7, 8, 9}

And the Venn diagram is: Question W4:

If Solve the following problems and draw Venn diagrams for each of them. M = {g, b, c}

N = {a, e, i, o, u}

P = {v, w, x, y, z}

(1) M N = {g, b, c} {a, e, i, o, u}

= {a, b, c, e, g, i, o, u}

And the Venn diagram is: (2) N P = {a, e, i, o, u} {v, w, x, y, z}

= { a, e, i, o, u, v, w, x, y, z}

And the Venn diagram is: (3) M P = {g, b, c} {v, w, x, y, z}

= { g, b, c, v, w, x, y, z}

And the Venn diagram is: (4) (M N) P = {g, b, c, a, e, i, o, u} {v, w, x, y, z}

(From (1) M N = { g, b, c, a, e, i, o, u })

= {a, b, c, e, g, i, o, u, v, w, x, y, z}

And the Venn diagram is: (5) M (N P) = {g, b, c} { a, e, i, o, u, v, w, x, y, z}

(From (2) N P = { a, e, i, o, u, v, w, x, y, z}

= { g, b, c, a, e, i, o, u, v, w, x, y, z}

And the Venn diagram is: Question W5:

In a class of 30 students, 20 of them are interested in mathematics, 25 students are interested in social science. Find out the number of students who are interested in both and show the same through a Venn diagram.

Total number of students in a class = 30

Total number of students interested in mathematics and social science = 20 + 25 = 45

Number of students interested in both mathematics and science = 45 − 30 = 15

And the Venn diagram is: Question W6.1:

In a group of students, D = {a, b, c, d, e, f} is the set of students participating in drama and M = {d, g, a, h} is the set of students participating in music.

Draw Venn diagrams for the given data:

The set of students participating only in drama

D = {a, b, c, d, e, f}

M = {d, g, a, h}

Set of students participating only in drama = D - (D M)

= {a, b, c, d, e, f}-({a, b, c, d, e, f} {d, g, a, h})

= {a, b, c, d, e, f} - {a, d}

= {b, c, e, f}

And the Venn diagram is: Question W6.2:

In a group of students, D = {a, b, c, d, e, f} is the set of students participating in drama and M = {d, g, a, h} is the set of students participating in music.

Draw Venn diagrams for the given data:

The set of students participating only in music

D = {a, b, c, d, e, f}

M = {d, g, a, h}

Set of students participating only in music = M- (M D)

= {d, g, a, h} - ({d, g, a, h} {a, b, c, d, e, f})

= {d, g, a, h} - {a, d}

= {g, h}

And the Venn diagram is: Question W6.3:

In a group of students, D = {a, b, c, d, e, f} is the set of students participating in drama and M = {d, g, a, h} is the set of students participating in music.

Draw Venn diagrams for the given data:

The set of students participating both in drama and music

D = {a, b, c, d, e, f}

M = {d, g, a, h}

Set of students participating both in drama and music = D M

= {a, b, c, d, e, f}{d, g, a, h}

= {a, d}

And the Venn diagram is: Question W6.4:

In a group of students, D = {a, b, c, d, e, f} is the set of students participating in drama and M = {d, g, a, h} is the set of students participating in music.

Draw Venn diagrams for the given data:

Total number of students participating either in drama or in music or both

D = {a, b, c, d, e, f}

M = {d, g, a, h}

Total number of students participating either in drama or in music, or both = D M

= {a, b, c, d, e, f}{d, g, a, h}

= {a, b, c, d, e, f, g, h}

And the Venn diagram is: Question O1:

Mention the laws which are applicable in the following situations. (a) The property used in is commutative property.

(b) The property used in is associative property.

Question W1.1:

If K L = L K

K = {11, 12, 13}

L = {12, 13, 14}

M= {13, 14, 15}

K L = {11, 12, 13} {12, 13, 14}

= {11, 12, 13, 14}

L K = {12, 13, 14} {11, 12, 13}

= {11, 12, 13, 14}

∴ K L = L K

Question W1.2:

If K M = M K

K = {11, 12, 13}

L = {12, 13, 14}

M= {13, 14, 15}

K M = {11, 12, 13} {13, 14, 15}

= {11, 12, 13, 14, 15}

M K = {13, 14, 15} {11, 12, 13}

= {11, 12, 13, 14, 15}

∴ K M = M K

Question W1.3:

If M L = L M

K = {11, 12, 13}

L = {12, 13, 14}

M= {13, 14, 15}

M L = {13, 14, 15} {12, 13, 14}

= {12, 13, 14, 15}

L M ={12, 13, 14} {13, 14, 15}

= {12, 13, 14, 15}

∴ M L = L M

Question W1.4:

If K L = L K

K = {11, 12, 13}

L = {12, 13, 14}

M= {13, 14, 15}

K L = {11, 12, 13} {12, 13, 14}

= {12, 13}

L K = {12, 13, 14} {11, 12, 13}

= {12, 13}

∴ K L = L K

Question W1.5:

If K M = M K

K = {11, 12, 13}

L = {12, 13, 14}

M= {13, 14, 15}

K M = {11, 12, 13} {13, 14, 15}

= {13}

M K = {13, 14, 15} {11, 12, 13}

= {13}

∴ K M = M K

Question W1.6:

If L M = M L

K = {11, 12, 13}

L = {12, 13, 14}

M= {13, 14, 15}

L M = {12, 13, 14} {13, 14, 15}

= {13, 14}

M L = {13, 14, 15} {12, 13, 14}

= {13, 14}

∴ L M = M L

Question W2.1:

If Prove that (X Y) Z = X (Y Z)

X = {10, 11, 12}

Y = {12, 13, 14}

Z = {14, 15, 16}

X Y = {10, 11, 12} {12, 13, 14}

= {12}

(X Y) Z = {12} {14, 15, 16}

= { }

= Φ

Y Z = {12, 13, 14} {14, 15, 16}

= {14}

X (Y Z) = {10, 11, 12} {14}

= { }

= Φ

∴ (X Y) Z = X (Y Z)

Question W2.2:

If Show that (X Y) Z = X (Y Z)

X = {10, 11, 12}

Y = {12, 13, 14}

Z = {14, 15, 16}

X Y = {10, 11, 12} {12, 13, 14}

= {10, 11, 12, 13, 14}

(X Y) Z = {10, 11, 12, 13, 14} {14, 15, 16}

= {10, 11, 12, 13, 14, 15, 16}

Y Z = {12, 13, 14} {14, 15, 16}

= {12, 13, 14, 15, 16}

X (Y Z) = {10, 11, 12} {12, 13, 14, 15, 16}

= {10, 11, 12, 13, 14, 15, 16}

∴(X Y) Z = X (Y Z)

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