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12th Odisha Board
IMPORTANT
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Give an example of a relation which is reflexive, symmetric but not transitive.

Important Questions on Relation and Function

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12th Odisha Board
IMPORTANT

Give an example of a relation which is reflexive, transitive but not symmetric

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12th Odisha Board
IMPORTANT

Give an example of a relation which is symmetric, transitive but not reflexive.

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12th Odisha Board
IMPORTANT

Give an example of a relation which is reflexive but neither symmetric nor transitive

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12th Odisha Board
IMPORTANT

Give an example of a relation which is transitive but neither reflexive nor symmetric

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12th Odisha Board
IMPORTANT

Give an example of a relation which is an empty relation.

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12th Odisha Board
IMPORTANT

Give an example of a relation which is a universal relation.

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12th Odisha Board
IMPORTANT

Let R be a relation on X, If R is symmetric then xRyyRx. If it is also transitive then xRy and yRxxRx. So whenever a relation is symmetric and transitive then it is also reflexive. What is wrong in this argument?

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12th Odisha Board
IMPORTANT

Suppose a box contains a set of n balls n4 (denoted by B) of four different colours (may have different sizes), viz. red, blue, green and yellow. Show that a relation R defined on B as R=b1,b2:balls b1 and b2 have the same colour is an equivalence relation. How many equivalence classes can you find with respect to R?
[Note: On any set X a relation R={x,y:x and y satisfy the same property P} is an equivalence relation. As far as the property P is concerned, elements x and y are deemed equivalent. For different P we get different equivalence relations on X]