Debunking a Conditional Statement: Providing a Counterexample to If a number is even, then it is divisible by 4

Counterexample of a conditional

In mathematics, a conditional statement is a statement of the form “if P, then Q” where P represents the antecedent or hypothesis and Q represents the consequent or conclusion

In mathematics, a conditional statement is a statement of the form “if P, then Q” where P represents the antecedent or hypothesis and Q represents the consequent or conclusion. To disprove a conditional statement, we need to provide a counterexample, which is an example that satisfies the hypothesis (P) but does not satisfy the conclusion (Q).

Let’s consider the conditional statement: “If a number is even, then it is divisible by 4.” We need to find a number that is even but not divisible by 4 to disprove this statement.

Counterexample: The number 6

Explanation:
– 6 is an even number because it can be divided by 2 without leaving a remainder.
– However, 6 is not divisible by 4 because when 6 is divided by 4, it leaves a remainder of 2.

Since 6 is an example that satisfies the hypothesis (being even) but does not satisfy the conclusion (not divisible by 4), it serves as a counterexample to this conditional statement.

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