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.
q = The food is good.
p = I eat too much.
If the food is not good, I won't eat too much.
Notq --> not p
I am not certain you can do this
q-->p as it is a logical fallacy.
~q = the food is not good
~p = I won't eat too much
~q -> ~p = If the food is not good, then I won't eat too much.
q. p. ~q. ~p. ~q -> ~p
T. T. F. F. T
T. F. F. T. T
F. T. T. F. F
F. F. T. T. T
"select the best match" -- I don't know what to do with that.
To write the statement using the symbols, we can use the following:
p = I eat too much
q = The food is good
Using these symbols, we can rewrite the statement as:
~q → ~p
Now, let's construct a truth table for this symbolic statement. The table will have columns for p, q, ~q (not q), ~p (not p), and ~q → ~p.
Here is the truth table:
| p | q | ~q | ~p | ~q → ~p |
|---|---|----|----|---------|
| T | T | F | F | T |
| T | F | T | F | T |
| F | T | F | T | F |
| F | F | T | T | T |
Now, let's match the truth table to the given options and find the best match. The options are:
A) p → q
B) ~p → q
C) q → ~p
D) ~q → ~p
Looking at the truth table, we can see that the only option that matches the table is option D) ~q → ~p.
Therefore, the best match for the given symbolic statement is:
D) ~q → ~p