Class 12 Mathematics

Relations And Functions

NCERT Solution of Math Exercise 1.1 (Part - 1)

Question – 1 – Determine whether each of the following relations are reflexive, symmetric and transitive.

(i) Relation R in the set A = {1, 2, 3, ..........., 13, 14} defined as class 12 math Relations and functions NCERT Solution1 Exercise 1.1

Solution:

class 12 math Relations and functions NCERT Solution2 Exercise 1.1

Thus, R is not reflexive

class 12 math Relations and functions NCERT Solution3 Exercise 1.1

Thus, R is not symmetric

class 12 math Relations and functions NCERT Solution4 Exercise 1.1

Therefore, R is not transitive

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


(ii) Relation of R in the set N of natural numbers defined as class 12 math Relations and functions NCERT Solution5 Exercise 1.1

Solution:

class 12 math Relations and functions NCERT Solution6 Exercise 1.1

Thus, R is not reflexive relation

class 12 math Relations and functions NCERT Solution7 Exercise 1.1

Thus, R is not symmetric

class 12 math Relations and functions NCERT Solution8 Exercise 1.1

Thus, R is not transitive.

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



(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} class 12 math Relations and functions NCERT Solution9 Exercise 1.1

Solution:

Given,R={(x,y):y is divisible by x} in A={1,2,3,4,5,6}

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

class 12 math Relations and functions NCERT Solution10 Exercise 1.1

Thus, R is reflexive.

class 12 math Relations and functions NCERT Solution11 Exercise 1.1

Thus, R is not symmetric.

class 12 math Relations and functions NCERT Solution12 Exercise 1.1

Thus, R is transitive.

Therefore, R is reflexive and transitive but not symmetric.

(iv) Relation R in the set Z of all integers defined as class 12 math Relations and functions NCERT Solution13 Exercise 1.1

Solution:

class 12 math Relations and functions NCERT Solution14 Exercise 1.1

In set Z of all integer.

class 12 math Relations and functions NCERT Solution15 Exercise 1.1

Therefore, R is reflexive relation.

class 12 math Relations and functions NCERT Solution16 Exercise 1.1

Therefore, R is symmetric.

class 12 math Relations and functions NCERT Solution17 Exercise 1.1

Therefore, R is transitive.

Thus, R is reflexive, symmetric and transitive.


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