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# NCERT Solutions Excercise 2

** Exercise – 2.2**

**1. Let A = {1, 2, 3, ……, 14}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0, where x, y Ð„ A}. Write its domain, Co domain and range.**

3x – y = 0

3x = y

(i) R = {(x, y) : 3x – y = 0, where x, y Ð„ A} = {(1, 3), (2, 6), (3, 9), (4, 12)}

(ii) Domain = {1, 2, 3, 4, 5,.…… 14}

(iii) Co domain = {1, 2, 3, 4, 5, ….. 4}

(iv) Range = {3, 6, 9, 12}

**2. Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural no. less than 4; x, y Ð„ N}. Depict the relationship using roster form write down the domain & the range.**

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

**(ii) Domain = {1, 2, 3}**

**(iii) Range = {6, 7, 8}**

**3. A = {1, 2, 3, 5} and = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference b/w x & y is odd ; x Ð„ A, y Ð„ B}. Write r in roster form**

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

**4. The fig 2.7 shows a relationship b/w the sets P & Q. write this relation**

**(ii) in roster form.**

**write its Domain & Range?**

**Sol****:- (i) **{x : x = y + 2}

**(iii) **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 {(a, b)} : a, b Ð„ A, b is exactly divisible by A}**

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

**(ii) Find the domain of r**

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

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

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

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

**6. Determine the domain and the range of the relation R defined by R = {x, x + 5) : x Ð„ {0, 1, 2, 3, 4, 5}}**

Domain = {0, 1, 2, 3, 4, 5}, Range = {5, 6, 7, 8, 9, 10}

**7. Write the relation R = {(x, x ^{3}) : x is a prime no less than 10} in roster form.**

Prime number less than 10 = (2, 3, 5, 7)

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

**8. Let A = {x, y, z} and B = {1, 2}. Find the no. of relations from A to B**

By using formula,

No. of relations = 2mn

= 2^{3 x 2} = 2^{6}

**9. Let R be the relation on Z defined by R = {(a, b) : a, b Ð„ Z, a – b is an integer}. Find the domain and the range of R.**

Domain = Z (Integers)

Range = Z (Integers)