Have a look at this webpage.
The only case that an implication is false is .
It is often said: A false statement implies any statement; a true statement is implied by any statement.
It's been years since high school, but I have been asked to help tutor. Please help me, because when I reviewed the material, I got confused.
"If I go to work, then I will get paid"
Hypothesis: "If I go to work" (P)
Condition: "I will get paid" (Q)
So, a truth table can be made: (And from here I interpret it as I think it should be)
P | Q | Result
T T T "I went to work, I got paid" Makes since, so its all true.
T F T "I went to work, I didn't get paid" Makes no since, so its all false.
F T T "I didn't go to work, I got paid"
F F T "I didn't go to work, I didn't get paid" Makes since, it's true.
The bolded statement I am confused on. Initially, I think it would all be false... But the high school provides an online tutor video, and they say, "If you cannot determine the truth, then it is true by default". I'm confused! Please help!
I'm sorry. I thought I got it, but then I lost it.
P implies Q. So, "If I work, then I get paid" is the statement we are working with, then how does If I don't work, then I get paid a true statement? That just doesn't make since! How is it just, by 'default', a true statement? My intuition tells me it is a FALSE statement.
Am I missing the big picture?
Lets remove the personal aspect here.
Take this sentence:
If it really rains hard then the grass will be wet.
Anyone who has lived in the American South has awaken early to find very wet grass but it did not rain overnight (heavy dew).
Does that make the original statement false?
Of course not!
If we have a true statement we must follow it with a true statement.
We don't give a darn what follows a false statement.