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Q: How is a relation between two sets defined?

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The relation, between two sets of objects, is a mapping which associates elements of the first set to those of the second set.

Cp-Cv is the relation of Mayer's formula. It can also be defined in words as the difference between two specific heat capacities.

Well, a rectangle is defined as having two sets of parallel sides and four right angles, a parallelogram is defined as having two sets of parallel sides and two sets of supplementary angles. Therefor, a rectangle is always, by definition, a parallelogram. A parallelogram is not always a rectangle, but it can be.

A relation is a mapping between elements of two sets - which need not be different sets. The relationship may be one-to-one or many-to-one but not one-to-many. In graphical form, any line which is parallel to the y-axis can meet the plot at most once.

Yes, you can consider it a relation between the points on the x-axis, and the points on the y-axis. In fact, ANY subset of R squared (in other words, any subset of the points on a plane), including the empty set, sets that contain single points, and larger sets, can be considered a relation in R squared (i.e., two sets of real numbers).

No, there is no relation between the two people.

The metric of a geometric space is defined as the distance between two points.

A relation is a mapping between two sets, a domain and a range. A function is a relationship which allocates, to each element of the domain, exactly one element of the range although several elements of the domain may be mapped to the same element in the range.

Parasitism can be defined as the relation between two different kinds of organisms in which one receives denifits from the other by causing damage to it. The damage is usually not fatal.

The union of a collection of sets is defined as the set of all distinct elements that are in the collection. This includes the specific case where the collection consists of two sets.

The high between the two

The relationship between energy and charge is potential difference or voltage. Where a volt is defined as existing between two points in an electric field when one joule of energy is required to move a charge of one coulomb between the two points.

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