Counterexample of a conditional
A counterexample of a conditional statement occurs when the statement is false despite the hypothesis being true
A counterexample of a conditional statement occurs when the statement is false despite the hypothesis being true. In other words, it contradicts the implication made by the conditional statement.
To provide an example, let’s consider the conditional statement: “If a number is divisible by 6, then it is even.” The hypothesis here is that the number is divisible by 6, and the implication is that the number is even.
However, we can easily find a counterexample to this statement by choosing a number that is divisible by 6 but not even. For instance, let’s take the number 15. It is divisible by 6 (15 divided by 6 equals 2, remainder 3), but it is clear that 15 is odd, not even.
Thus, we have found a counterexample to the conditional statement “If a number is divisible by 6, then it is even,” since the hypothesis is true but the conclusion is false in this case.
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