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 :(
I'll exercise if I eat too much.
can be rephrased as:
IF "I eat too much" THEN "I'll exercise"
≡ IF p THEN q.
Can you continue?
no....still lost with how to construct the table....
The truth table is a standard table for the conditional that you can find from any textbook or notes.
For p->q, it is false ONLY when p is true and q is false, the 3 other cases are all true.
Yes, you're correct. The symbolic statement for "I'll exercise if I eat too much" can be represented as q → p.
To construct a truth table, you need to consider all possible combinations of truth values for the variables p and q. Since there are two variables, p and q, each with two possible truth values (true or false), the truth table will have 2^2 = 4 rows.
Here's how you can construct the truth table for q → p:
1. Start by listing all possible truth value combinations for p and q:
p | q
-----------------
true | true
true | false
false | true
false | false
2. Determine the truth value of q → p for each combination. Remember that q → p is only false when q is true and p is false; otherwise, it is true.
p | q | q → p
------------------------------
true | true | true
true | false | true
false | true | false
false | false | true
So, the truth table for q → p is as follows:
p | q | q → p
--------------------------
true | true | true
true | false | true
false | true | false
false | false | true
From this truth table, we can observe that "q → p" is true in three cases and false in one case.
Now, to select the best match for this statement, let's analyze the options:
- p ∧ q: The statement "p ∧ q" means both p and q are true. However, this does not accurately represent the original statement. In the truth table, there are cases where q is false, but p is true, and vice versa.
- p ∨ q: The statement "p ∨ q" means either p or q (or both) is true. This also does not accurately represent the original statement. In the truth table, there are cases where both p and q are false, but the statement is still true.
- p → q: The statement "p → q" means if p is true, then q must be true. This is not the same as the original statement "I'll exercise if I eat too much." In the original statement, q (I'll exercise) depends on p (I eat too much), not the other way around.
Hence, the best match for the symbolic statement "q → p" is the original statement "I'll exercise if I eat too much."