The document NCERT Solution - Relations and Functions (Ex - 2.2) JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 11.

All you need of JEE at this link: JEE

**NCERT QUESTIONS**

**(Ex - 2.2) **

**Ques 1: ****Let A = {1, 2, 3, â€¦ , 14}. Define a relation R from A to A by R = {( x, y): 3x â€“ y = 0, where x, y âˆˆ A}. Write down its domain, codomain and range.**

**Ans: **The relation R from A to A is given as

R = {(*x*, *y*): 3*x* â€“ *y* = 0, where *x*, *y* âˆˆ A}

i.e., R = {(*x*, *y*): 3*x* = *y*, where *x*, *y* âˆˆ A}

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

The domain of R is the set of all first elements of the ordered pairs in the relation.

âˆ´Domain of R = {1, 2, 3, 4}

The whole set A is the codomain of the relation R.

âˆ´Codomain of R = A = {1, 2, 3, â€¦, 14}

The range of R is the set of all second elements of the ordered pairs in the relation.

âˆ´Range of R = {3, 6, 9, 12}

**Ques 2: ****Define a relation R on the set N of natural numbers by R = {( x, y): y = x + 5, x is a natural number less than 4; x, y âˆˆ N}. Depict this relationship using roster form. Write down the domain and the range.**

**Ans: **R = {(*x*, *y*): *y* = *x* + 5, *x* is a natural number less than 4, *x*, *y* âˆˆ **N**}

The natural numbers less than 4 are 1, 2, and 3.

âˆ´R = {(1, 6), (2, 7), (3, 8)}

The domain of R is the set of all first elements of the ordered pairs in the relation.

âˆ´ Domain of R = {1, 2, 3}

The range of R is the set of all second elements of the ordered pairs in the relation.

âˆ´ Range of R = {6, 7, 8}

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

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

R = {(*x*, *y*): the difference between *x* and *y* is odd; *x* âˆˆ A, *y* âˆˆ B}

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

**Ques 4: ****The given figure shows a relationship between the sets P and Q. write this relation**

**(i) in set-builder form (ii) in roster form.**

**What is its domain and range?**

**Ans: **According to the given figure, P = {5, 6, 7}, Q = {3, 4, 5}

(i) R = {(*x, y*): *y = x* â€“ 2; *x* âˆˆ P} or R = {(*x, y*): *y = x* â€“ 2 for *x* = 5, 6, 7}

(ii) R = {(5, 3), (6, 4), (7, 5)}

Domain of R = {5, 6, 7}

Range of R = {3, 4, 5}

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

**{( a, b): a, b âˆˆ 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.**

**Ans: **A = {1, 2, 3, 4, 6}, R = {(*a*, *b*): *a*, *b* âˆˆ A, *b* is exactly divisible by *a*}

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

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

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

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

**Ans: **R = {(*x*, *x* + 5): *x* âˆˆ {0, 1, 2, 3, 4, 5}}

âˆ´ R = {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}

âˆ´Domain of R = {0, 1, 2, 3, 4, 5}

Range of R = {5, 6, 7, 8, 9, 10}

**Ques 7: ****Write the relation R = {( x, x^{3}): x is a prime number less than 10} in roster form.**

**Ans: **R = {(*x*, *x*^{3}): *x* is a prime number less than 10}

The prime numbers less than 10 are 2, 3, 5, and 7.

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

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

**Ans: **It is given that A = {*x*, *y*, z} and B = {1, 2}.

âˆ´ A Ã— B = {(*x*, 1), (*x*, 2), (*y*, 1), (*y*, 2), (*z*, 1), (*z*, 2)}

Since *n*(A Ã— B) = 6, the number of subsets of A Ã— B is 2^{6}.

Therefore, the number of relations from A to B is 2^{6}.

**Ques 9: ****Let R be the relation on Z defined by R = {( a, b): a, b âˆˆ Z, a â€“ b is an integer}. Find the domain and range of R.**

**Ans: **R = {(*a*, *b*): *a*, *b* âˆˆ **Z**, *a* â€“ *b* is an integer}

It is known that the difference between any two integers is always an integer.

âˆ´Domain of R = **Z**

Range of R = **Z**

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

158 videos|186 docs|161 tests