Question 1: Which of the following are examples of empty set?

(i) Set of all even natural numbers divisible by .

(ii) Set of all even prime numbers

(iii) and is rational

(vi) is a natural number , and simultaneously

(v) is a point common to any two parallel lines

Answer:

(i) Set of all even natural numbers divisible by would mean a set . This has elements and therefore not an empty set.

(ii) Set of all even prime numbers would me a set . This has elements and therefore not an empty set.

(iii) and is rational . This would mean that . is irrational number. Hence this is an empty set.

(vi) is a natural number , and simultaneously . There are no number which are less than and also greater than simultaneously. Hence this is an empty set.

(v) is a point common to any two parallel lines . This is an empty set because two parallel lines never intersect.

Question 2: Which of the following sets are finite and which are infinite?

(i) Set of concentric circles in a plane.

(ii) Set of letters of the English Alphabets.

(iii)

(iv)

(v)

(vi)

Answer:

(i) Set of concentric circles in a plane: There can be infinite concentric circles. Therefore this is an INFINITE set.

(ii) Set of letters of the English Alphabets: There are only 26 English alphabets

Hence this is a FINITE set.

(iii) . This would be a set . There will be infinite elements in the set. Therefore this is an INFINITE set.

(iv) . This set will contain . Hence this is an FINITE set.

(v) . This set would be . There will be infinite elements in the set. Therefore this is an INFINITE set.

(vi) . This set would include all decimals, rational numbers and irrational numbers between and . There will be infinite elements in the set. Therefore this is an INFINITE set.

Question 3: Which of the following sets are equal?

(i)

(ii)

(iii)

(vi)

Answer:

*Note: EQUAL SETS – Two sets and are said to be equal if every element of is a member of , and every element of is a member of .*

Set is

this can also be written as as repeating element can be eliminated.

is

Hence

Question 4: Are the following sets equal?

(i) is a letter in the word reap

(ii) is a letter in the word paper

(iii) is a letter in the word rope

Answer:

Therefore none of them are equal.

Question 5: From the sets given below, find the pair the equivalent sets:

Answer:

*EQUIVALENT SETS: Two finite sets and are equivalent if their cardinal numbers are same. i.e. .*

Therefore

and are equivalent sets.

Question 6: Are the following pairs of sets equal? Give reasons

(i) , is a solution of

Answer:

(i)

is a solution of

Therefore NOT EQUAL.

(ii) is a letter of the word

is a letter of the word

Hence and are EQUAL.

Question 7: From the sets given below, select equal sets and equivalent sets

Answer:

Hence we can see that and are equal. Also and are equal sets.

and are equivalent. Also and are equivalent sets. Also and are equivalent.

Question 8: Which of the following sets are equal?

Answer:

Therefore and

They are also all equivalent sets as they all have elements each.

Question 9: Show that the set of letters needed to spell and the set of letters needed to spell are equal.

Answer:

Therefore they are equal sets as they have the same elements. They are also equivalent sets.