**Questions 1. Which of the following are examples of the null set? **

**i) Set of odd natural numbers divisible by 2**

**Solution:**

Yes, this is a null set because three is no odd natural number divisible by 2.

Note:A set which does not contain any element is called thenull set.

**ii) Set of even prime numbers**

**Solution: **

No, this is not a null set because 2 is an even number which is prime.

**iii) {x : x is a natural numbers, x < 5 and x > 7}**

**Solution:**

Yes, this is a null set because three is no natural number which is less than 5 and greater than 7.

**iv) {y : y is a point common to any two parallel lines}**

**Solution:**

Yes, this is a null set because two parallel lines have no points in common because they do not intersect.

**Question 2. Which of the following sets are finite or infinite? **

**i) The set of months of a year**

**Solution: **

This is a

finiteset because there is only 12 months in a year.

Note:A set which is empty or consists of a definite number of elements is calledfiniteotherwise, the set is calledinfinite.

**ii) {1, 2, 3, …}**

**Solution:**

This is an

infiniteset because there will always be a new number if we add 1 to the previous number, or we can say that it is a set of natural numbers and there are infinite natural numbers.

**iii) {1, 2, 3, …, 99, 100}**

**Solution:**

This is a

finiteset because there is only 100 numbers in the set.

**iv) The set of positive integers greater than 100**

**Solution:**

This is an

infiniteset because there are infinite positive integers greater than 100 which can be generated by adding 1 to the previous number.

**v) The set of prime numbers less than 99**

**Solution:**

This is a

finiteset because prime numbers which are less than 99 are finite.

**Question 3. State whether each of the following set is finite or infinite:**

**i) The set of lines which are parallel to the x-axis**

**Solution:**

Infinite.We can draw infinite parallel lines with respect to the x-axis.

**ii) The set of letters in the English alphabet**

**Solution: **

Finite.There are only 26 letters in the English alphabet.

**iii) The set of numbers which are multiples of 5**

**Solution:**

Infinite.There are infinite numbers which are multiple of 5 namely {5, 10, 15 ——-}

**iv) The set of animals living on the earth**

**Solution:**

Finite.The animals Living on the earth can be counted they are not infinite.

**v) The set of circles passing through the origin (0, 0)**

**Solution:**

Infinite.We can draw infinite number of circles passing through the origin with different radius.

**Question 4. In the following, state whether A = B or not:**

**i) A = {a, b, c, d} B = {d, c, b, a}**

**Solution:**

Yes.Every element of A is also an element of B and every element of B is also an element of A namely {a, b, c, d}.

Note:Two sets A and B are said to be equal if they have exactly the same elements, and we writeA = B. Otherwise, the sets are said to be unequal, and we writeA ≠ B.Order in which elements appear does not matter.

**ii) A = {4, 8, 12, 16} B = {8, 4, 16, 18}**

**Solution: **

No.12 is an element that is present in A but not in B and similarly 18 is an element present in B not in A.

**iii) A = {2, 4, 6, 8, 10} B = {x : x is positive even integer and x ≤ 10}**

**Solution:**

Yes.If we define set B it can be written like this {2, 4, 6, 8, 10} and therefore every element of A is also an element of B and every element of B is also an element of A.

**iv) A = {x : x is a multiple of 10}, B = {10, 15, 20, 25, 30, …}**

**Solution:**

No.If we define B we can clearly see that {-40, -30, -20, -10, 0}. All these numbers are also multiples of 10, and they are not in set B. Hence A ≠ B.

**Question 5. Are the following pair of sets equal? Give reasons**

**i) A = {2, 3}, B = {x : x is solution of x**^{2 }+ 5x + 6 = 0}

^{2 }+ 5x + 6 = 0}

**Solution:**

No.By solving the equation x

^{2 }+ 5x + 6,x

^{2 }+ 5x + 6 = 0x

^{2 }+ 2x + 3x + 6 = 0(x + 2)(x + 3) = 0

x = -2, -3

Now it is clear that B can be defined as {-2, -3}.

Now -2, -3 are not in A and also 2, 3 is not in set B. Hence A ≠ B.

**ii) A = {x : x is a letter in the word FOLLOW} B = {y : y is a letter in the word WOLF}**

**Solution: **

Yes.It is clear that A can be defined as {F, O, L, W} an if we define B, {F, O, L, W}. Now it is clear that every element of A is also an element of B and every element of B is also an element of A namely {W, O, L, F}.

**Question 6. From the sets given below, select equal sets :**

**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 & E = G.

Note:Two sets A and B are said to be equal if they have exactly the same elements.

For A, 8∈ A, but 8∉ B,8∉ B,8∉ D,8∉ E, 8∉ F,8∉ G,8∉ H,Hence, A is not equal to B, D, E, F, G, H.

Also, 2∈ A, but 2∉ C Hence A, ≠ C.

For B, 2∈ B, but 2∉ C,2∉ E,2∉ F,2∉ G, 2∉ H.Hence, B is not equal to C, E, F, G, H.

Also, Every element of B can be found in D namely {1, 2, 3, 4} and vice-versa is also true. Hence

B = D.

For C, 14∈ C, but 14∉ D,14∉ E,14∉ F,14∉ G, 14∉ H.Hence C is not equal to D, E, F, G, H.

For D, 2∈ D, but 12∉ E,2∉ F,2∉ G, 2∉ H.Hence D is not equal to E, F, G, H.

For E, -1∈ E, but -1∉ F, -1∉ H.Hence E is not equal to F, H.

Also, Every element of E can be found in G namely {-1, 1} and vice-versa is also true. Hence

E = G.

For F,0∈ F, but 0∉ G, 0∉ H.Hence F is not equal to G, H.

For G, -1∈ G, but -1∉ H.Hence G is not equal to H.

So, we can observe that only

B = D & E = G.

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