Inverse of a Theorem

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Inverse of a Theorem

 

the theorem obtained when the hypothesis and conclusion of a given initial theorem are replaced by their negations. For example, the theorem “If the sum of the opposite angles of a quadrangle is equal to 180°, a circle can be circumscribed about the quadrangle” has the inverse “If the sum of the opposite angles of a quadrangle is not equal to 180°, a circle cannot be circumscribed about the quadrangle.” The inverse of a theorem is equivalent to the theorem’s converse.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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