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 :(
Yes, the statement "I'll exercise if I eat too much" can be represented symbolically as q -> p, where p represents "I eat too much" and q represents "I'll exercise".
To construct a truth table, you need to consider all possible combinations of truth values for p and q.
Since p and q are both simple statements, there are only two possibilities for each statement: true (T) or false (F).
In this case, we have:
p (I eat too much) q (I'll exercise) q -> p (I'll exercise if I eat too much)
T T T
T F T
F T F
F F T
To determine the truth value of q -> p, you can use the following logical rules:
- If both p and q are true, then q -> p is true.
- If p is true and q is false, then q -> p is true.
- If p is false and q is true, then q -> p is false.
- If both p and q are false, then q -> p is true.
Looking at the truth table, you can see that when q is true (T) and p is true (T), q -> p is also true (T). For all other combinations, q -> p is true (T) as well.
Therefore, the truth table for q -> p is:
p q q -> p
T T T
T F T
F T F
F F T
For the best match, you can select the truth table option that matches the truth values obtained from the table. In this case, the best match would be "t t f t".
Yes, you're correct. The symbolic representation of the statement "I'll exercise if I eat too much" is q → p.
To construct a truth table, we need to consider all possible combinations of truth values for p and q.
Since there are two variables (p and q), there are 2^2 = 4 rows in the truth table.
First, let's list all the possible combinations of truth values for p and q:
1. p = True, q = True
2. p = True, q = False
3. p = False, q = True
4. p = False, q = False
Now, let's evaluate the truth value of q → p for each combination:
1. q → p = True → True = True
2. q → p = False → True = True
3. q → p = True → False = False
4. q → p = False → False = True
The completed truth table is as follows:
| p | q | q → p |
|-----|-----|--------|
| T | T | T |
| T | F | T |
| F | T | F |
| F | F | T |
Among the given options, the truth table for q → p matches the one we constructed.