Basic number theory question and answers

Question 1

Question:   List the elements of the following sets.

Answer:    i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i}
ii) There are exactly two such names {Karnataka, Kerala}

Question 2

Question:   List the elements of the following sets and specify whether they are finite or infinite:

Answer:    (i) Since there is no natural number lying between 2 and 3, the set is a null set i.e. f. This is a finite set.
(i) Since there are infinite number of real number between 4 and 1, the set is an infinite set.
(iii) Since there are infinite number of multiplies of 4 i.e. {4,8,12,16....}, the set is an infinite set.
(iv) Although the set is finite at any given time, it would be almost impossible to list its elements.

Question 3

Question:   Write down the following statements using set notation.
(i) x is an element of set A
(ii) y is not an element of set
(iii) A is a subset of B
(iv) A is a proper subset of B
(v) A contains B
(vi) A is superset of B
(vii) Neither A is a subset of B, nor B is a subset of A.

Answer:   

Question 4

Question:   Express the following sets in set builder form.
(i) Set A consists of the letters p, q, r, s and t
(ii) Set C = {1,3,5,7,....}
(iii) Set D = {8}

Answer:   

Question 5

Question:   If A = {2,3}, B = {3,4,5}, C = {3,4,6}, find

Answer:   

Question 6

Question:   A = {a, b, c, e}; B = {b, c, d, e, f}; C = {d, e, f, g}

Answer:    (i)

(ii)

(iii)

(iv)

Question 7

Question:  

Answer:   

Question 8

Question:  
Compute

Answer:   

Question 9

Question:   Let A = {1, 2, 3}, B = {2, 3, 4, 5} and C = {3, 4, 5, 6} be three subsets of the universal set U = {1, 2, 3, 4, 5, 6, 7}. Verify the following identities

Answer:   

Question 10

Question:   For any two sets A and B, prove that A' - B' = B - A.

Answer: