Question

Determine whether or not the following relations have the properties of the relations. Be sure to...

Determine whether or not the following relations have the properties of the relations. Be sure to justify your answers.

a) R = {(x, y)| y is a biological parent of x} on the set of all people

b) R = {(x, y) ∈ N × N | lcm(x, y) = 10}

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Answer #1

A relation is said to be relation in mathematical terms, if it is well defined. In other words, one should be able to decide without any ambiguity that two elements are related or not.

For example, if we consider the cities nearby to Delhi, then this relation is not well defined, because the word "nearby" is not well defined itself.

On the other hand, if we consider the the cities which are within 100 Km of Delhi, the this represents a relation because the distance 100 Km is well defined.

a) R = {(x, y)| y is a biological parent of x} on the set of all people

Here R is a relation because it is well defined that a person is biological parent of other or not. There is no ambiguity in statement.

b) R = {(x, y) ∈ N × N | lcm(x, y) = 10}

Here R is a relation because the it is can be decided without ambiguity that lcm of two given numbers is 10 or not.

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