TYPES OF SETS WORKSHEET

Question 1: 

Find the cardinal number of the following sets.

(i) M = {p, q, r, s, t, u}

(ii) P = {x : x = 3n + 2, n∈W and x < 15}

(iii) Q = { y : y = 4/3n, n ∈ N and 2 < n ≤ 5}

(iv) R = {x : x is an integers, x ∈ Z and –5 ≤ x < 5}

(v) S = The set of all leap years between 1882 and 1906.

Solution

Question 2 : 

Identify the following sets as finite or infinite.

(i) X = The set of all districts in Tamilnadu.

(ii) Y = The set of all straight lines passing through a point.

(iii) A = { x : x ∈ Z and x < 5}

(iv) B = {x : x²–5x+6 = 0, x ∈N}

Solution

Question 3 :

Which of the following sets are equivalent or unequal or equal sets?

(i) A = The set of vowels in the English alphabets.

B = The set of all letters in the word “VOWEL”

(ii) C = {2, 3, 4, 5}

D = { x : x ∈ W, 1 < x < 5}

(iii) E = The set of A={ x : x is a letter in the word “LIFE”}

F = {F, I, L, E}

(iv) G = {x : x is a prime number and 3 < x < 23}

H = {x : x is a divisor of 18

Solution

Question 4 :

Identify the following sets as null set or singleton set.

(i) A = {x : x ∈N, 1 < x < 2}

(ii) B = The set of all even natural numbers which are not divisible by 2

(iii) C = {0}.

(iv) D = The set of all triangles having four sides.

Solution

Question 5 :

State which pairs of sets are disjoint or overlapping?

(i) A = {f, i, a, s} and B={a, n, f, h, s}

(ii) C = {x : x is a prime number, x >2} and D ={x:x is an even prime number}

(iii) E = {x : x is a factor of 24} and F={x : x is a multiple of 3, x < 30}   

Solution

Question 6 : 

 If S = {square, rectangle, circle, rhombus, triangle}, list  the elements of the following subset of S.

(i) The set of shapes which have 4 equal sides.

(ii) The set of shapes which have no sides.

(iii) The set of shapes in which the sum of all interior angles is 180^o

(iv) The set of shapes which have 5 sides.

Solution

Question 7 : 

If A = {a, {a, b}}, write all the subsets of A.

Solution

Question 8 : 

Write down the power set of the following sets.

(i) A = {a, b}

(ii) B = {1, 2, 3}

(iii) D = {p, q, r, s}

(iv) E = ∅         

Solution

Question 9 :

Find the number of subsets and the number of proper subsets of the following sets.

(i) W  =  {red, blue, yellow}

(ii) X = { x² : x ∈ N, x² ≤ 100} 

Solution

Question 10 :

If n(A) = 4, find n [P(A)].

(ii)  If n(A) = 0, find n [P(A)].

(iii) If n[P(A)] = 256, find n(A).  

Solution

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us : 

v4formath@gmail.com

We always appreciate your feedback. 

You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6