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.
Is it q->p?? I do not know how to do the truth table :(
Think of it this way first before attempting to do the problem in detail. If someone tells you:
"I'll exercise if I eat too much."
then when can you say that this person is not sticking to what he/she said?
still have no idea....
To symbolize the statement "I'll exercise if I eat too much" using p and q, you can represent it as q -> p. The arrow symbol (->) represents the implication or conditional relationship between q and p, meaning that q implies p.
To construct a truth table for this symbolic statement, you need to evaluate the possible combinations of truth values for p and q. Since there are two variables (p and q), there are four possible combinations:
1. When both p and q are true (T):
- q: T
- p: T
2. When p is true (T) and q is false (F):
- q: F
- p: T
3. When p is false (F) and q is true (T):
- q: T
- p: F
4. When both p and q are false (F):
- q: F
- p: F
Now, let's construct the truth table for the symbolic statement q -> p:
| q | p | q -> p |
| --- | --- | ------ |
| T | T | T |
| F | T | T |
| T | F | F |
| F | F | T |
In this truth table, q -> p is true (T) in three out of the four possible combinations, except when p is false (F) and q is true (T). Therefore, the statement "I'll exercise if I eat too much" is best represented by the symbolic statement q -> p.
Hope that helps!