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**Exercise 2.2**

**1. Let A = {1, 2, 3, ……., 14}. Define a relation R from A to A by R = **** where **** Write down its domain co-domain and range.**

**Ans.** Given: A = {1, 2, 3, ……….., 14}

The ordered pairs which satisfy are (1, 3), (2, 6), (3, 9) and (4, 12).

R = {(1, 3), (2, 6), (3, 9), (4, 12)}

Domain = {1, 2, 3, 4}

Range = {3, 6, 9, 12}

Co-domain = {1, 2, 3, ……….., 14}

**2. Define a relation R on the set N of natural numbers R = **** is a natural number less than 4: **** Depict this relationship using roster form. Write down the domain and the range.**

**Ans. **Given: R =

Putting = 1, 2, 3 in we get = 6, 7, 8

R = {(1, 6), (2, 7), (3, 8)}

Domain = {1, 2, 3}

Range = {6, 7, 8}

**3. A = {1, 2, 3 5} and B = {4, 6, 9}. Define a relation R from A to B by R = **** the difference between **** and **** is odd: **** Write R in roster form.**

**Ans. **Given: A = {1, 2, 3, 5} and B = {4, 6, 9}, A, B

= (1 – 4), (1 – 6), (1 – 9), (2 – 4), (2 – 6), (2 – 9), (3 – 4), (3 – 6) (3 – 9),

(5 – 4), (5 – 6), (5 – 9)

R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6) (5, 4), (5, 6)}

**4. Figure shows a relationship between the sets P and Q. Write this relation:**

**(i) in set-builder form**

**(ii) roster form**

**What is its domain and range?**

**Ans. (i)** Relation R in set-builder form is R =

**(ii)** Relation R in roster form is R = {(5 3), (6, 4), (7, 5)

Domain = {5, 6, 7}

Range = {3, 4, 5}

**5. Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by **** is exactly divisible by **

**(i) Write R in roster form.**

**(ii) Find the domain of R.**

**(iii) Find the range of R.**

**Ans. **Given: A = {1, 2, 3, 4, 6}

A set of ordered pairs where is exactly divisible by

**(i) **R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (4, 6)}

**(ii) **Domain of R = {1, 2, 3, 4, 6}

**(iii) **Range of R = {1, 2, 3, 4, 6}

**6. Determine the domain and range of the relation R defined by**

**R = **

**Ans. **Given: R = =

and

Putting we get

Domain of R = {0, 1, 2, 3, 4 5}

Range of R = {0, 1, 2, 3, 4 5}

**7. Write the relation R = **** is a prime number less than **** in roster form.**

**Ans. **Given: R =

Putting = 2, 3, 5, 7

R = {(2, 8), (3, 27), 5, 125), (7, 343)}

**8. Let A = **** and B = {1, 2}. Find the number of relations from A to B.**

**Ans. **Given: A = and B = {1, 2}

Number of elements in set A = 3 and Number of elements in set B = 2

Number of subsets of

Number of relations from A to.

**9. Let R be the relation on Z defined by R = **** is an integer}. Find the domain and range of R.**

**Ans. **Given: R =

=

=

Domain of R = Z

Range of R = Z

Very helpful?thanks for your great work?