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Part 1
Determine if the following statement is true or false.
A theorem cannot have counterexamples.
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Part 1
Choose the correct answer.
A.
False, a theorem is a conjecture that can be strengthened by additional information or proven to be false by a counterexample.
B.
True, a theorem is based on deductive reasoning and cannot have counterexamples.
C.
True, a theorem is based on inductive reasoning and cannot have counterexamples.
D.
False, although a theorem cannot be strengthened by additional information, but it can be proven false by a counterexample.
1 answer
The correct answer is:
A. False, a theorem is a conjecture that can be strengthened by additional information or proven to be false by a counterexample.
This is true because, by definition, a theorem is a statement that has been proven based on previously established statements, such as other theorems, and axioms. A statement that is proven false by a counterexample indicates that it is not a theorem.
