Sets And Relations

Step 1: Checking Reflexivity.
For the relation to be reflexive,

x%3Cx%5E2

must hold for all

x%20%5Cin%20%5Cmathbb%7BR%7D

. However, for some values of

x

, such as

x%20%3D%200

, this condition is not satisfied. Therefore, the relation is not reflexive. Step 2: Checking Symmetry.
For symmetry, if

(x%2C%20y)%20%5Cin%20R

, then

(y%2C%20x)

must also be in

R

. But if

x%3Cy%5E2

, it is not necessarily true that

y%3Cx%5E2

. Therefore, the relation is not symmetric. Step 3: Checking Transitivity.
For transitivity, if

(x%2C%20y)%20%5Cin%20R

and

(y%2C%20z)%20%5Cin%20R

, then

(x%2C%20z)

must also be in

R

. This does not hold for all values of

x

y

, and

z

, so the relation is not transitive. Step 4: Conclusion.
Thus, the correct answer is (D) Neither reflexive nor symmetric nor transitive.

Chapter Questions
1 MCQs