It messed with my head a lot as well. The answer is that it's not possible for ¬Drive Home AND Rains to be true. This is because if Rains were true, then due to the first implication, Drive Home must also be true. Therefore, if ¬Drive Home is true, then Rains must be false.

If the statement is true, the contrapositive is true: if !Drive Home -> !Rain. So provided with the fact that I didn’t drive home, you can infer it didn’t rain.

Your interpretation is wrong then. We have that rain -> drive home; here is the truth table.

    rain | drive | rain->drive home
    false| drive | true
    true | drive | drive

Thus, the statement could be true, if you have driven home, but you did not provide such information.

Just because something is on the right hand side of an implication doesn't make it true. The statement A=>B is true iff A is false, or A is true and B is true at the same time.

Or alternatively, (not rain) || drive home

    rain | not rain | drive home | (not rain) || drive home
    true | false    | true       | true
    true | false    | false      | false
    false| true     | true       | true
    false| true     | false      | true

So it is entirely possible to not have rained, and not to have driven home.

The contrapositive is !drive home -> !rain

    (drive home) | rain | !(drive home) | !rain | !(drive home) -> !rain
    true         | false| false         | true  | true
    true         | true | false         | false | true
    false        | false| true          | true  | true
    false        | true | true          | false | false

Thus whether the statement is true depends entirely on whether it rained; but you can not infer that as both options yield a true statement.

This whole thread and chain is affirming the consequent.

> In propositional logic, affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "if the lamp were broken, then the room would be dark"), and invalidly inferring its converse ("the room is dark, so the lamp must be broken"), even though that statement may not be true. This arises when the consequent ("the room would be dark") has other possible antecedents (for example, "the lamp is in working order, but is switched off" or "there is no lamp in the room").

> Converse errors are common in everyday thinking and communication and can result from, among other causes, communication issues, misconceptions about logic, and failure to consider other causes.

https://en.wikipedia.org/wiki/Affirming_the_consequent

Wouldn't that only be affirming the consequent if it were the following?:

> If it rains, I drive home. I drove home. Therefore, it rained. <-- logical fallacy

Because, for example, you could've driven home for some other reason. But that wasn't the statement.

> If it rains, I drive home. I didn't drive home. Therefore, it didn't rain.

How could it possibly have rained without violating the statement "If it rains, I drive home." given you didn't drive home?

Ugh I messed up last night. GP is correct.

This is false. I messed up last night when writing this. Sorry.