**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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