Which is the best definition of a counterexample?
a. An example that proves a statement is true.
b. An example that shows a statement is true for only the (k + 1) term.
c. An example that proves a statement is true only for the n = k term.
d. An example that shows a statement is not true.

Any exception to a generalization is referred to as a counterexample. A counterexample disproves a generalization in logic, and it does so rigorously in mathematics and philosophy.

An example that contradicts a statement (shows that it is false). For instance, the assertion "all dogs are hairy" may be shown wrong by locating a single hairless dog (the counterexample), as seen below.

To demonstrate, you must discover an integer n such that n² is divisible by 4, but n is not divisible by 4 — the "if" portion must be true, but the "then" part must be false. Consider the number n = 6. Then n2 = 36 is divisible by 4, although n = 6 is not. As a result, n = 6 is a contradiction to the assertion.

Since a counterexample is an example that makes the statement false. Therefore, the best definition of a counterexample is An example that shows a statement is not true.

Hence, the correct option is "An example that shows a statement is not true".

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Which is the best definition of a counterexample? a. An example that proves a statement is true. b. An example that shows a statement is true for only the (k + 1) term. c. An example that proves a statement is true only for the n = k term. d. An example that shows a statement is not true.

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What is a counterexample?

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Which is the best definition of a counterexample?
a. An example that proves a statement is true.
b. An example that shows a statement is true for only the (k + 1) term.
c. An example that proves a statement is true only for the n = k term.
d. An example that shows a statement is not true.