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Posting on Behalf of a 7Sage User: I have a question regarding conditional reasoning.

Mary - Student ServiceMary - Student Service Member Administrator Student Services
in Logical Reasoning 808 karma

Consider the following statement: A good apple is a ripe apple, and an apple will not be picked unless it is ripe.

We can come up with two diagrams here: 1) picked apple --> ripe apple 2) good apple --> ripe apple

I understand it is not possible to form a conditional chain in this case. However, is it possible to say: picked apple + good apple --> ripe apple?

I am asking this question because the answer to this question requires me to understand that we can say -ripe -> -good + - picked. Could you explain both statements using + to me? Thank you.

Sharing this on behalf of a fellow 7Sage user. Any help and answers would be incredibly appreciated! Thanks a bunch!

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  • hank2023hank2023 Alum Member
    62 karma

    If you wanted to express these two conditional statements in a single statement, you would write (picked or good) --> ripe. This keeps the information from the original conditional relationships without adding anything else.

    (picked and good) --> ripe does not work because it is more restrictive than the two original conditional relationships were separately. If an apple must be both picked and good in order to be ripe, we lose the possibility for an apple to be ripe just because it was picked or just because it was good (these were both possible from the original conditional relationships).

    Additionally, when taking the contrapositive of conditionals with and/or components, or becomes and, and and becomes or. E.g. for (A and B ) --> C, the contrapositive is ~C --> (~A or ~B ). Here I'm using "~" to mean "not. For the apple example, the contrapositive of (picked or good) --> ripe is ~ripe --> ~picked and ~good.

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