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| Math Central | Quandaries & Queries |
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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
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