# Basic Discrete math question

1. Jan 8, 2015

### MarcL

Before I make a fool of myself let me just say I just had my first class today and the book/ teacher aren't helpful in my question. And I'm not even sure I'm in the right section, this is just my major

1. The problem statement, all variables and given/known data

"If 1+1=3 then 2+2=4"

2. Relevant equations
We just covered conditional statement and its truth table that states if p is false and q is true, then the statement is still true

3. The attempt at a solution

Basic question, following the table given to us, but it doesn't makes sense to me. If 1+1=3 then 2+2=4 , how can the whole statement be true?

2. Jan 8, 2015

### Staff: Mentor

Yes
To quote what you wrote above,

3. Jan 8, 2015

### MarcL

WHat I was trying to say is that, it doesn't make sense to me ( how i see it ) that if I state 1+1 = 3 then 2+2=4 then why would the whole statement be true if only half of it is in realitiy.

4. Jan 8, 2015

### Staff: Mentor

To re-quote what you wrote above,
p: 1 + 1 = 3 (false)
q: 2 + 2 = 4 (true)
$p \Rightarrow q$ (true)

From the truth table for an implication, the only pair of values of p and q that make the implication false are when p is true and q is false. All other pairs of values for p and q yield a true implication.

Last edited: Jan 8, 2015
5. Jan 8, 2015

### haruspex

I think the important point is being missed.
Let S be the statement "if p then q". If it turns out that p is false then the statement S is true regardless of whether q is true.
Thus "if 1+1=3 then 2+2=9" is also a true statement.
To put it in everyday language, if you start from a false premise then you can deduce anything.
It is possible that the questioner wants you to illustrate this by a chain of argument that starts with "1+1=3" as a given and ends with "2+2=4". Or, better, ends with "2+2=9".
Here's how you could do the last one:
1+1=3
2+2 = 1+1+1+1 = (1+1)(1+1) = (1+1)2 = 32 = 9

6. Jan 8, 2015

### Staff: Mentor

I could be wrong, but that's not my take on this problem, which is to recognize that p (1 + 1 = 3) is false, so no matter what q is, the overall implication is true.

7. Jan 8, 2015

### haruspex

Yes, I said it was just a possibility. Without seeing the original question verbatim it's hard to know.
But the main point I wanted to make is that this
is misleading by being insufficiently general. It should say
if p is false then the statement is true regardless of the truth or falsehood of q​

8. Jan 9, 2015

### RUber

The truth of the statement is based on the truth or falsehood of the logic, not the parts. The logic is $p \implies q$. If p is not true, then the logic is true by virtue of the fact it cannot be proven false. There is a large gap between true and useful logic. This logic is true but totally useless, since p is never true.