**The domain of definition of the function is**

(A) [1,4]

(B) [1,0]

(C) [0,5]

(D) [5,0]

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Solution: (A)

Given that

For domain of ,

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**Let be a relation on the set The relation is**

(A) a function

(B) transitive

(C) not symmetric

(D) reflexive

**View Answer**

Solution: (C)

Since, and So, R is not a function.

Since, and but So, R is not transitive

Since, but so, R is not symmetric

Since, so, R is not reflexive

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**The domain of the function **

(A)

(B)

(B)

(B)

**View Answer**

Answer: (B)

Explanation:

We must have

This is only possible when

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**Let R be a relation defined as if . Then, the relation is(**A) Reflexive

(B) Symmetric

(C) Transitive

(D) None of these

**View Answer**

Answer: (B)

is not reflexive since

is symmetric since if , then

Thus

R is not transitive. For example,

consider the numbers 3, 7, 3.

since and , so we have and

But 3 is not related to 3 as .

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