Contradiction Question help

Hi guys, I’m stuck on 6.14. I know we are supposed to use Ana Con for reasoning for two sentences to introduce there’s a contradiction but I’m getting a little stuck with what to do after that. Has anyone worked on it?

5 thoughts on “Contradiction Question help

  1. Samantha Valone

    Hi everyone – I took another look at this problem today. For me, it helped to prove that SameRow(d,f) using disjunction elimination. Then use contradiction introduction to contradict Cube(f). In the final step I was able to use negation introduction to prove the goal. Hopefully this gives some guidance!

  2. Nathan MacDonald

    Hi Julia (and all),

    Something that helped me was the fact that after proving a contradiction and citing a contradiction introduction, the next step within that subproof can be literally anything using the contradiction elimination rule. In other words, if an assumption in a subproof is a contradiction to a premise, then any statement can logically follow within that subproof. I was able to use this fact to eventually lead me to a disjunction elimination for my final step.

    I hope this helps!


  3. Samantha Valone

    I also did subproofs for SameRow(b,f) and SameRow(c,f) and contradicted them. I am stuck on where to go from there. I am not sure if I need to then prove that ¬SameRow(d,f) is false in order to prove SameRow(d,f) is true. Then I was thinking of doing a subproof starting with the premise Cube(f), and disprove SameRow(d,f) ∧ Cube(f). So then ¬Cube(f) would follow. If anyone has any suggestions please let me know. Thanks!

  4. Rachel Horowitz-Benoit

    This the last problem I’m still struggling with; every step in my proof gets a checkmark, including when I restate the goal at the end, but I am still getting an X in the goal strip, and when I click, a message that says “You may not use the Ana Con rule to satisfy this goal.” Did anyone else run into the same thing?

    I basically used subproofs to prove that two of the predicates in the first premise could not be true, and therefore that the third one must be true; I then used this to prove that Cube(f) must be false to justify the negation symbol before the last premise.

  5. Elizabeth Sheedy

    Hi Julia,

    I’m also having trouble with 6.14. So far, I’ve made subproofs for SameRow (b.f) and SameRow (c,f) and have shown the contradictions of these given the other premises. You want to make sure that at the end of each subproof, you are showing that f is not a cube, since that is our end goal. ⊥ Elim is helpful when asserting that f is not a Cube, since the ⊥ Elim rule allows us to assert any sentence following a contradiction (LPL p. 161). Let me know if you have any questions; I hope this helps.

    Sincerely, Liz

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