Exercise 1.2
Question 1. Which of the following are the example of the null set.
(I) Set of odd natural numbers divisible by 2.
(II) Set of even prime number.
(III) { x : x is a natural numbers, x<5 and x>7}
(IV) { y : y is a point common to any two parallel lines}
Solution. (I), (III) and (IV) are the example of null sets.
Question 2. Which of the following sets are finite or infinite sets.
(I) The set of months of the years.
(II) {1,2,3,4,.........}
(III) {1,2,3,4,........100}
(IV) The set of positive integer greater than 100.
(V) The set of prime numbers less than 99.
Solution. Finite Set = (I), (III) and (V)
Infinite Set = (II) and (IV)
Question 3. State whether each of the following set is finite or infinite.
(I) The set of lines which are parallel to x-axis.
(II) The set of English Alphabet.
(III) The set of numbers which are multiple of 5.
(IV) The set of animal living on earth.
(V) The set of circle passing passing through the origin(0,0).
Solution. Finite Set = (II) and (IV)
Infinite Set = (I), (III) and (V)
Question 4. In the following, State whether A=b or not.
(I) A={a,b,c,d} and B={d,c,b,a}
(II) A={4,8,12,16} and B={8,4,16,18}
(III) A={2,4,6,8,10} and B={ x : x is positive integer and x<=10}
(IV) A={ x : x is multiple of 10} and B={10,15,20,25,30,............}
Solution. Yes= (I) and (III)
No= (II) and (IV)
Question 5. Are the following pair of sets are equal? Give Reason.
(I) A={2,3} and B={ x : x is solution of x^2+5x+6}
Solution. Above pair of sets are not equal because the equation x^2+5x+6, it has a solution (-3,-2). (2,3) is not a solution because on putting value of x we don't get 0.
(II) A={ x : x is a letter of the word FOLLOW} and B={ y : y is a letter in the word WOLF}
Solution. The answer is yes because the set A has all letter in set B.
Question 6. From the set given below, select equal set.
A={2,4,8,12} B={1,2,3,4}, C={4,8,12,14}, D={3,1,4,2}, E={-1,1}, F={0,a}, G={1,-1}, H={0,1}
Solution. B=D and E=G