True conditonal statement with false converse [duplicate]

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Is it possible to have a true conditional statement with a false converse? If there is does anyone have an example of one? or why doesn't one exist?

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2 Answers

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Consider the statement: "If it rains, then it is wet." The converse is false.

For a math statement: "If a function is differentiable, then it is continuous."

For a non calculus statement: "If $4$ divides a number then that number is even." (Brian Scott came up with the same example in the comments)

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There is a widely employed distinction between necessary ($B \rightarrow A$) and sufficient ($A \rightarrow B$) conditions:

a) If you get an 'A' you will pass the exam. (sufficient, but not necessary)

b) If there's fire then there's oxygen. (necessary, but not sufficient)

You are probably looking for statements where both conditions hold, namely, biconditional statements.

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