Logic
Logical reasoning forms a basis for much rational reasoning, and so constitutes another category of mathematical foundations.
Elements
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1.4.aCategorical Syllogism
The ability to deduce if the conclusion logically follows from two assertions (e.g., "A is in C and B is in A, is B in C?").
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1.4.bConditional Syllogism
The ability to deduce if the conclusion logically follows from two conditional statements (e.g., "If A then B and if B then C, if A then C?").
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1.4.cLogical Equivalence of Contrapositive
The ability to deduce that logical statements and their contrapositives are logically equivalent (e.g., "If $A$, then $B$" is equivalent to "if not $B$, then not $A$").