**Define a set. Give examples to illustrate the difference between a collection and a set**

Solution:

**Definition: **A set is a collection of well defined objects. The objects of a set are called elements or members of the set.

**Examples: **

a) The collection set of all prime numbers between 100 and 200.

b) The collection of all planets in the universe.

c) The collection of all fair people in the city

Here (a) and (b) are examples of sets but (c) is not one cannot define fair.

**Which of the following collection are sets?**

**(a) All the students of your school. **

**(b) Members of Indian parliament. **

**(c) The colures of rainbow. **

**(d) The people of Karnataka having green ration card. **

**(e) Good teachers in a school **

**(f) Honest persons of your village. **

Solution:

(a), (b) and (c) are sets.

(d), (e) and (f) are not sets.

**Represent the following sets in roster method:**

**(a) Set of all alphabet in English language. **

**(b) Set of all odd positive integers less than 25. **

**(c) The set of all odd integers. **

**(d) The set of all rational numbers divisible by 5. **

**(e) The set of all colors in the Indian flag. **

**(f) The set of letters in the word ELEPHANT. **

**Solution:**

** **(a) A = {a, b, c……..x, y, z}

(b) Z = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23}

(c) P = {±1, ±3, ±5….}

(d) R = {5, 10, 15……}

(e) Y = {saffron, white, green}

(f) S = {E, L, P, H, A, N, T}

**Represent the following sets by using their standard notations.**

**(a) Set of natural numbers **

**(b) Set of integers **

**(c) Set of positive integers **

**(d) Set of rational numbers **

**(e) Set of real numbers **

Solution:

(a) N = {1, 2, 3……}

(b) Z = {0, ±1, ±2, ±3…….}

(c) Z + = {1, 2, 3…….}

(d) Q = {p/q, p, q z and q ≠ 0}

(e) R = (Q U Z}

**Write the following sets in set builder form:**

**(a) {1, 4, 9, 16, 25, 36} **

**(b) {2, 3, 5, 7, 11, 13, 17, 19, 23……} **

**(c) {4, 8, 12, 16, 20, 24……} **

**(d) {1, 4, 7, 10, 13, 16……} **

Solution:

(a) A = {x: /x=k^{2} for some k€N, 1 ≤ k ≤6}

(b) P = {x/x is a prime number}

(c) X = {x/x is a multiple of 4}

(d) Z = {x/x=3n – 2 when n = 1, 2, 3…..}

**State whether the set is finite or infinite:**

**(a) The set of all prime numbers. **

**(b) The set of all sand grains on this earth. **

**(c) The set of points on a line. **

**(d) The set of all school in this world. **

Solution:

(a) infinite set

(b) finite set

(c) Infinite set

(d) finite set

**Check whether the sets A and B are disjoint**

**(a) A is the set of all even positive integers. B is the set of all prime numbers. **

**(b) A = {3, 6, 9, 12, 15……} **

**B = {19, 24, 29, 34, 39……..} **

**(c) A is the set of all perfect squares; B is the set of all negative integers. **

**(d) A = {1, 2, 3} and B = {4, 5,{1, 2, 3}} **

**(e) A is the set of all hydrogen atoms in this universe; B is the set of all water molecules on earth. **

Solution:

(a) A and B are not disjoint sets since A ∩ B = {2}

(b) A and B are not disjoint since A ∩ B = {24….}

(c) A and B are disjoint.

(d) A ∩ B = {1, 2, 3}. Hence they are not disjoint.

(e) A and B is disjoint.

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