** ****Q.1: Which of the following are sets. Explain your answer.**

**(a). The collection of all day in a week which have the first letter S.**

**Answer**:

In a year we can easily identify all the days in a week which starts with the **letter S.** So it will form a clearly defined collection of objects.

**Hence, the given collection can be a set.**

**(b). The collection of ten most famous singers of India.**

**Answer:**

If we talk about the most **famous singers** then it is not a well-defined collection, because there are different parameters to be famous. So, it does not fall in this category.

**Hence, the given collection cannot be a set.**

**(c). A group of best football strikers of the world.**

**Answer:**

A group of best **football strikers** cannot be determined because each individual have different point of view to identify the best football strikers. So it does not form a well-defined collection.

**Hence, this group is not a set.**

**(d). The collection of all girls in your school.**

**Answer:**

The collection of all **girls** in your school can easily be identified as this category is clearly defined.

**Hence, the given collection can be a set.**

**(e). The collection of all odd numbers below 50.**

**Answer:**

The collection of all **odd numbers below 50** can be identified by calculating, so it forms a well-defined collection. .

**Hence, the given collection can be a set.**

**(f). A collection of poems written by the poet Shakespeare. **

**Answer:**

A collection of all the **poems written by Shakespeare** can be identified easily as he has the copyright on all his poems. So it forms a well-defined collection.

**Hence the given collection can be a set.**

**(g). The collection of all prime numbers.**

**Answer:**

All **prime numbers** can be identified after doing some calculations and thus it forms a well-defined collection.

**Hence, the given collection can be a set.**

**(h). The collection of questions in science book.**

**Answer:**

We can find out the given **question in a science book**, so it will form a well-defined collection of objects.

**Hence, the given collection can be a set.**

**(i). A collection of most dangerous reptiles in India.**

**Answer:**

If we are talking about the most **dangerous reptiles in India**, and then it would be difficult to tell. This category will vary from person to person. So it does not fall in the category of well-defined collection.

**Hence, the given collection cannot be a set.**

** **

**Q.2: Let P = {2, 3, 4, 5, 6, 7}. Insert the correct symbol ∈or∉ inside the given blank spaces below:**

**(a). 2 . . . . . . . . . . P **

**(b). 9 . . . . . . . . . P **

**(c). 11 . . . . . . . . P**

**(d). 4 . . . . . . . . P **

**(e). 0 . . . . . . . . P **

**(f). 7 . . . . . . . . P**

**Answer:**

**(a). **

**(b). **

**(c).**

**(d).**

**(e).**

**(f).**

**Q.3: Write the given sets in roster form:**

**(a). P = {y: y is an integer and -4 < y < 6}.**

**(b). Q = {y: y is a natural number which is <8}**

**(c). R = {y: y is a 2 digit natural number in which the sum of its digits is 9}**

**(d). S = {y: y is a prime number which is a divisor of 70}**

**(e). T = The set of all letters in the word ELEPHANT**

**(f). U = The set of all letters in the word DIVISION**

**Answer:**

**(a).** **P = {y: y is an integer and -4 < y < 6}**

The elements from this given set are **–3, –2,-1, 0, 1, 2, 3, 4, and 5 o**nly.

Hence, we can write the following set in the **roaster form** as given below:

**P = {–3, –2,-1, 0, 1, 2, 3, 4, 5}**

**(b).** **Q = {y: y is a natural number which is <6}**

The elements from this given set are **1, 2, 3, 4, 5, 6, and 7** only.

Hence, we can write the following set in the **roaster form** as given below:

**Q = {1, 2, 3, 4, 5, 6, 7}**

**(c).** **R = {y: y is a 2 digit natural number in which the sum of its digits is 9}**

The elements from this given set are **18, 27, 36, 45, 54, 63, 72, 81 and 90** only.

Hence, we can write the following set in the **roaster form** as given below:

**R = {18, 27, 36, 45, 54, 63, 72, 81, 90}**

**(d).** **S = {y: y is a prime number which is a divisor of 140}**

70 = 2 x 2 x 5 x 7

The elements from this given set are **2, 5, and 7** only.

Hence, we can write the following set in the **roaster form** as given below:

**S = {2, 5, 7}.**

**(e).** **T = The set of all letters in the word ELEPHANT**

There are 8 letters in the given word **ELEPHANT**, out of which L is repeated.

Hence, we can write the following set in the **roaster form** as given below:

**T = {E, L, P, H, A, N, T}**

**(f).** **U = The set of all letters in the word DIVISION**

There are 8 letters in the given word **DIVISION**, out of which I is repeated.

Hence, we can write the following set in the **roaster form** as given below:

**U = {D, I, V, S, O, N}**

**Q.4: Write the given sets in set-builder form:**

**(a). {4, 8, 12, 16, 20}**

**(b). {3, 9, 27, 81}**

**(c). {4, 16, 64, 256, 1024}**

**(d). {1, 3, 5, 7…}**

**(e). {1, 8, 27, 64….1000}**

** **

**Answer:**

**(a). {4, 8, 12, 16, 20} = {y: y = 4n, n∈Pand1≤n≤5}**

**(b). {3, 9, 27, 81}**

We can see here that

Hence, {3, 9, 27, 81} = {y: y = 3^{n},

**(c). {4, 16, 64, 256, 1024}**

We can see here that

Hence, {4, 16, 64, 256, 1024} = {y: y = 4^{n},

**(d). {1, 3, 5, 7…}**

Above mentioned that the numbers are the set of **odd natural numbers.**

Hence, {1, 3, 5, 7…} = {y: y is an odd natural numbers}

**(e). {1, 8, 27, 64….1000}**

We can see here that

Hence, {1, 8, 27, 64….1000} = {y: y = n^{2},

**Q.5: List all the elements from the given sets:**

**(a). P = {y: y is even natural number}**

**(b). Q = {y: y is an integer, −12<y<92}**

**(c). R = {y: y is an integer; y2≤4}**

**(d). S = {y: y is letter in the word “TIFFIN”}**

**(e). T = {y: y is a month of a year having 31 days}**

**(f). U = {y: y is a consonant in the English alphabet which precedes m}**

**Answer**:

**(a). P = {y: y is even natural number} = {2, 4, 6, 8, 10 …..}**

**(b). Q =** {y: y is an integer,

We can see that

**Hence, Q = {0, 1, 2, 3, 4}**

**(c). R = {y: y is an integer; y2≤4}**

We can see that

**Hence, R = {-2, -1, 0, 1, 2}**

**(d). S = {y: y is letter in the word “TIFFIN”} **

** = {T, I, F, N}**

**(e). T = {y: y is a month of a year having 31 days}**

** = {January, March, May, July, September, November}**

**(f). U = {y: y is a non-vowel alphabet in English which comes before m}**

** = {b, c, d, f, g, h, j, k, l}**

** **

** **

**Q.6: Match the following:**

** **

(A) |
{1, 2, 3, 6} |
(i) |
{y: y is a divisor of 6 and also a prime number} |

(B) |
{T, R, I, G, O, N, M, E, Y} |
(ii) |
{y: y is less than 10 and also an odd number} |

(C) |
{2, 3} |
(iii) |
{y: y is natural number divisor of 6} |

(D) |
{1, 3, 5, 7, 9} |
(iv) |
{y: y is a letter of the word TRIGONOMETRY} |

** ****Answer:**

(A) |
{1, 2, 3, 6} | (iii) |
{y: y is natural number divisor of 6} |

(B) |
{T, R, I, G, O, N, M, E, Y} | (iv) |
{y: y is a letter of the word TRIGONOMETRY} |

(C) |
{2, 3} | (i) |
{y: y is a divisor of 6 and also a prime number} |

(D) |
{1, 3, 5, 7, 9} | (ii) |
{y: y is less than 10 and also an odd number} |