Class 12 Maths

Relation and Function

NCERT Solution

Exercise 1.1 Part 2

(v) Relation R in the set A of human beings in a town at a particular time given by

class 12 math Relations and functions NCERT Solution18 Exercise 1.1

Solution:

class 12 math Relations and functions NCERT Solution19 Exercise 1.1

And thus, R is reflexive.

class 12 math Relations and functions NCERT Solution20 Exercise 1.1

Thus, R is symmetric.

class 12 math Relations and functions NCERT Solution21 Exercise 1.1

Therefore, R is transitive

Thus, R is reflexive, symmetric and transitive.


class 12 math Relations and functions NCERT Solution22 Exercise 1.1

Solution: Since, x and x both live in the same locality,

class 12 math Relations and functions NCERT Solution23 Exercise 1.1

Therefore, R is reflexive.

Since, x and y both live in the same locality

class 12 math Relations and functions NCERT Solution24 Exercise 1.1

This means y and x both also live in the same locality

Therefore, R is symmetric

class 12 math Relations and functions NCERT Solution25 Exercise 1.1

Thus, R is transitive.

Thus, R is reflexive, symmetric and transitive.

class 12 math Relations and functions NCERT Solution26 Exercise 1.1

Solution: Here, x is not exactly 7 cm taller than x

class 12 math Relations and functions NCERT Solution27 Exercise 1.1

Thus, R is not reflexive

Now, x is exactly 7 cm taller than y, thus, y is not exactly 7 cm taller than x.

class 12 math Relations and functions NCERT Solution28 Exercise 1.1

Thus, R is not symmetric,

Again, x is exactly 7 cm taller than y and y is exactly 7 cm taller than z, then x would not be 7 cm taller than z

Thus, R is not transitive relation.

Therefore, R is neither reflexive nor transitive and nor symmetric.



class 12 math Relations and functions NCERT Solution29 Exercise 1.1

Solution: Here, it is clear that x is not the wife of x

class 12 math Relations and functions NCERT Solution30 Exercise 1.1

Again, here x is wife of y, but y is not wife of x

class 12 math Relations and functions NCERT Solution31 Exercise 1.1

Thus, R is not symmetric

class 12 math Relations and functions NCERT Solution32 Exercise 1.1

Thus, R is not transitive.

Therefore, R is neither reflexive nor transitive and nor symmetric.

class 12 math Relations and functions NCERT Solution33 Exercise 1.1

Solution: Here, it is clear that x is not the father of x

class 12 math Relations and functions NCERT Solution34 Exercise 1.1

Again, here x is father of y, but y is not father of x

class 12 math Relations and functions NCERT Solution35 Exercise 1.1

Thus, R is not symmetric

class 12 math Relations and functions NCERT Solution36 Exercise 1.1

Thus, R is not transitive.

Therefore, R is neither reflexive nor transitive and nor symmetric.



Exercise 1

Exemplar Problems