Question 442965: Write the statement in symbols using the p and q given below. Then construct a truth table for the symbolic statement and select the best match.
p = I eat too much
q = I'll exercise.
I'll exercise if I eat too much. (Points : 5)
Mutiple Choice
1.) q right pointed arrow p
p q q right pointed arrow p
T T T
T F T
F T F
F F T
2.) P right pointed arrow and q
p q p right pointed arrow and q
T T F
T F T
F T F
F F F
3.) q right pointed arrow and p
p q q and right pointed arrow and p
T T F
T F T
F T T
F F T
4.) p right pointed arrow and q
p q q and right pointed arrow q
T T T
T F F
F T T
F F F
Please indicate which is correct, 1,2,3 or 4.
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! I'll exercise if I eat too much.
You can rewrite this as: "If I eat too much, then I'll exercise."
This means p -> q.
To elaborate:
By saying this you are saying if p happens, then q will happen
That is to say, p implies q, which is usually stated as p -> q.
To construct a truth table:
p q p->q
T T T
T F F
F T T
F F T
It may be weird to think that a false statement implying a true statement is a truth. But consider this statement.
If it rains, I'm going to sleep all day.
So if it rains, and then I sleep all day, it's true.
If it it rains, and then I don't sleep all day, I've lied. It's false.
Now what if it doesn't rain? I never said anything about that. No matter what I do, you can't prove that I lied. So, the condition is always true if the initial condition is false.
so F->T = T F->F = T.
The truth table should be:
p q p->q
T T T
T F F
F T T
F F T
It seems that #4 is close, make sure you don't have a typo.
I think #4 is your answer, you just didn't type a T in that last spot.
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