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The following is a textbook question that stumped me as there is no more information given. Is this statement true or false?

$\{ x : x \text{ is a triangle in a plane} \}$ is a subset of $\{ x : x\text{ is a rectangle in the plane} \}$.

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Tricky question ! Because a rectangle with one side zero can be a triangle ! – lsp Apr 5 '13 at 6:51


Can you think of a triangle that's not a rectangle?

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This is false. Since rectangles are not triangles and triangles are not rectangles, the two sets are disjoint and therefore neither set is a subset of the other.

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Its true because two triangles combine to form a rectangle. So the set of rectangle would contain two triangles. And therefore a triangle is a subset of a rectangle.

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In general, $x, y \in X \implies x \cup y \in X$ is false. For example, consider $ x = \{0\}, y = \{1\}, X = \{x, y\}$. So your reasoning is incorrect. – Orat Sep 14 '13 at 5:43

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