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[–] antiracist ago 

You prolly have a book or something. Ask me questions from there.

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[–] eagleshigh [S] ago 

I'll do it from memory because I don't see anything in the book.

So (A ^ B) <-> C)=1 A=1 B=1 C=0 so (1 ^ 1) is 1 then (1 <-> 0) is 0 so it's false. This is a valid argument as it's opposite from the conclusion in comparison to if it was the correct conclusion which would make it invalid right?

How would I find the counterexample for that?

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[–] JesusOfNazareth62 ago  (edited ago)

Let's say @Bojangles said ((A ^ B) <-> C) was true, or always true (a tautology), and he challenged you to find a counterexample.

You have one. Where A and B are true but C is false.

Are there other counterexamples?

We have three terms, A, B, and C. That means there are 8 possible truth values for them. If there was A, B, C, D, there would be 16 possibilities. Get that?

So, how many of the 8 possibilities makes ((A ^ B) <-> C) false? Those are the counterexamples.

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[–] antiracist ago 

Your questions aren't making sense to me. There is no argument here, only one proposition. There are no "counterexamples" since you gave the truth values and that proposition is false with those values.