Stephanie is doing an indirect proof with three given statements and one conclusion. How many of these statements could be false based on her assumption to contradict the assumption and prove the original conclusion?

Question

Stephanie is doing an indirect proof with three given statements and one conclusion.  How many of these statements could be false based on her assumption to contradict the assumption and prove the original conclusion?

across · Answer

Let $a\text{ and }b\text{ and }c\implies d$. There are many ways to prove this indirectly. One of them is to assume the contrapositive: $\neg d\implies\neg a\text{ or }\neg b\text{ or }\neg c$, in which case all of $a$, $b$, and $c$ would have to be true for the whole statement to hold water. But what do you exactly mean with "based on her assumption to contradict the assumption?" Another way would be to set the whole statement up as a contradiction, as follows: $a\text{ and }b\text{ and }c\text{ and }\neg d$, in which case no individual statement can be false at all.

across · Answer

Notice how, in both cases, no individual statement can be false! But it would be better if you could clarify that for me. :)

anonymous · Answer

Stephanie thinking that her initial theory is wrong.

anonymous · Answer

You were right, thank you! :)