Let be the set of all real numbers and be a relation in , defined by :

1.	Let be the set of all real numbers and be a relation in , defined by : R = {(a, b) ∶ a ≤ b2 }. Verify that is a function or not.
Answer» Let be the set of all real numbers. And relation on set S is defined as = {(a, b) ∶ a ≤ b² }. Since, 1, 2 and 3 are real numbers, therefore, 1, 2 and 3 ∊ S. Now, 1 ≤ 4 = 2² and 1 ≤ 9 = 3². ⇒ 1 ≤ 2²and 1 ≤ 3². ⇒ (1, 2) ∊ R and (1, 3) ∊ R. (By definition of relation ) Therefore, relation R is not function. (Because, in function every element have unique images.) Hence, relation R = {(a,b): a ≤ b²on set of all real numbers is not a function.

Let be the set of all real numbers and be a relation in , defined by : R = {(a, b) ∶ a ≤ b2 }. Verify that is a function or not.

Answer»

Let be the set of all real numbers.

And relation on set S is defined as = {(a, b) ∶ a ≤ b² }.

Since, 1, 2 and 3 are real numbers, therefore, 1, 2 and 3 ∊ S.

Now, 1 ≤ 4 = 2² and 1 ≤ 9 = 3².

⇒ 1 ≤ 2²and 1 ≤ 3².

⇒ (1, 2) ∊ R and (1, 3) ∊ R. (By definition of relation )

Therefore, relation R is not function. (Because, in function every element have unique images.)

Hence, relation R = {(a,b): a ≤ b²on set of all real numbers is not a function.

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Let be the set of all real numbers and be a relation in , defined by : R = {(a, b) ∶ a ≤ b2 }. Verify that is a function or not.

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