How to correctly format proofs?

[mharten1]

Homework Statement

Hi, I'm taking a mathematical proofs class and I'm having trouble formatting my proofs correctly. We haven't done any proofs in class yet, but some simple proofs are due in this week's homework assignment. I've tried using the internet to help me, but all the hits that I get are very confusing.

Homework Equations

Suppose:
(1) A v (B ^ C)
(2) B → D
(3) C → E
(4) D ^ E → A v C
(5) ~A (~ is the not symbol, I don't know how to type it and I don't see it on the quick symbols)

Then C is true.

The Attempt at a Solution

This seems like a really easy proof. Correct me if I'm wrong, but because you know that A is not true, (B ^ C) must be true. Thus, we have already proven that C is true. If this is the correct way to prove this, can someone please help me format it into a formal proof? Thanks.

 

[Mark44]

Homework Statement

Hi, I'm taking a mathematical proofs class and I'm having trouble formatting my proofs correctly. We haven't done any proofs in class yet, but some simple proofs are due in this week's homework assignment. I've tried using the internet to help me, but all the hits that I get are very confusing.

Homework Equations

Suppose:
(1) A v (B ^ C)
(2) B → D
(3) C → E
(4) D ^ E → A v C
(5) ~A (~ is the not symbol, I don't know how to type it and I don't see it on the quick symbols)

Then C is true.

The Attempt at a Solution

This seems like a really easy proof. Correct me if I'm wrong, but because you know that A is not true, (B ^ C) must be true. Thus, we have already proven that C is true.

And that B must be true.

So at this point you have A is false, B is true, and C is true. Now use the other given statements to arrive at the conclusion.

BTW, ~ is perfectly fine for the negation operator.

If this is the correct way to prove this, can someone please help me format it into a formal proof? Thanks.

For a formal proof, you should justify each statement that you make. For instance, when you start off by saying that A is false, the justification is statement 5 of the hypotheses (the statements that are given, and that you can assume to be true).

 

[mharten1]

And that B must be true.

So at this point you have A is false, B is true, and C is true. Now use the other given statements to arrive at the conclusion.

BTW, ~ is perfectly fine for the negation operator.


For a formal proof, you should justify each statement that you make. For instance, when you start off by saying that A is false, the justification is statement 5 of the hypotheses (the statements that are given, and that you can assume to be true).

Thanks for your response. Why is it necessary to keep going, haven't I already proved C to be true? Nevertheless, here's what I would do next.

Because B is true, it follows from statement 2 that D is also true.
Because C is true, it follows from statement 3 that E is also true.

Then, because D and E are true, from statement 4 we get A v C. Because we know from statement 5 that A is false, C must be true.

But wasn't this redundant, because I already knew C was true?

 

[Mark44]

The only statements that are important in the proof are 1 and 5, with 2, 3, and 4, seeming to me to be red herrings, so you really don't need to continue.

However, it seems to me that you skipped some steps, one of which I already pointed out; namely, that B ^ C being true implies that both B and C must be true. From that you can conclude that C is true.