Sets — Practice

Question 1

Which of these are sets? (i) the collection of all the months of a year beginning with the letter J (ii) the collection of ten most talented writers of India.

Accepted Answer

(i) is a set; (ii) is not

Question 2

Write C = {x : x is a two-digit natural number such that the sum of its digits is 8} in roster form.

Accepted Answer

C = {17, 26, 35, 44, 53, 62, 71, 80}

Question 3

State which of these are empty sets: (i) the set of lines passing through a given point (ii) the set of odd natural numbers divisible by 2 (iii) the set of even prime numbers.

Accepted Answer

(i) not empty (ii) empty (iii) not empty

Question 4

Find the cardinality of C, where C is the set of letters in the word INDIA.

Accepted Answer

n(C) = 4

Question 5

List all the subsets of B = {p, q}.

Accepted Answer

the empty set, {p}, {q}, {p, q}

Question 6

If A = {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15}, find A minus B and B minus A.

Accepted Answer

A minus B = {2, 4, 8, 10} and B minus A = {3, 9, 12, 15}

Question 7

If A = {0, 2, 4}, find A intersection the empty set, and A intersection A. What do you notice?

Accepted Answer

A intersection the empty set = the empty set; A intersection A = A

Question 8

State with a reason whether {2, 3, 5, 7, 9} equals {x : x is a prime number}.

Accepted Answer

Not equal, because 9 is not prime

Question 9

Write E = {x : x = 2n squared + 1, where n is an integer and -3 is at most n and n is at most 3} in roster form.

Accepted Answer

E = {1, 3, 9, 19}

Question 10

State whether each is finite or infinite: (i) the set of prime numbers smaller than 99 (ii) the set of lines that can be drawn parallel to the X-axis (iii) the set of circles passing through the origin.

Accepted Answer

(i) finite (ii) infinite (iii) infinite

Question 11

Let A be the naturals, B the even naturals, C the odd naturals and D the primes. Find A intersection B, B intersection C and B intersection D.

Accepted Answer

A intersection B = the even naturals; B intersection C = the empty set; B intersection D = {2}

Question 12

With A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20} and C = {2, 4, 6, 8, 10, 12, 14, 16}, find A minus C, B minus C and C minus B.

Accepted Answer

A minus C = {3, 9, 15, 18, 21}; B minus C = {20}; C minus B = {2, 6, 10, 14}

Question 13

Show that the set of letters in ASSASSINATION and the set of letters in STATION are equal.

Accepted Answer

Both are {A, S, I, N, T, O}, so each is a subset of the other and the sets are equal

Question 14

List all the subsets of E = {1, 4, 9, 16}, and say how many there are.

Accepted Answer

Sixteen subsets, from the empty set to E itself

Question 15

In a class survey, 23 students like cricket, 18 like badminton and 9 like both. Using the counting rule the chapter's last Think-and-discuss box points at, how many like at least one of the two? If the class has 40 students, how many like neither?

Accepted Answer

32 like at least one; 8 like neither

Question 16

Write {1, 4, 9, 16, 25, ..., 100} in set-builder form, and explain why 'x is a square number and x is at most 10' will not do.

Accepted Answer

{x : x = n squared, n is a natural number and n is at most 10}

Practice — Sets

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