   SEARCH HOME Math Central Quandaries & Queries  Question from Tront: So, there's a general rule that all squares are rectangles but not all rectangles are squares. I'm trying to find a term that would describe this relationship. I've found that if all of A is B but not all B is A then I'd say that A is a subset of B, but is there a term that describes the relationship as a whole? I don't want to describe the components, I want to describe the relationship as a whole. Hi Tront,

I think the term you want is logical implication.

There are different, equivalent definitions of a rectangle and a square. Here are two of them.

Rectangle:

A rectangle is a quadrilateral with 4 right angles.

Square:

A square is a quadrilateral with 4 sides of equal length and 4 right angles.

If a plane figure is a square then a logical implication of this is that it is also a rectangle.

To prove this implication assume that a plane figure $F$ is a square. Then $F$ is a quadrilateral with 4 sides of equal length and 4 right angles. Hence $F$ is a quadrilateral and it has 4 right angles. Thus $F$ is a square.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.