Logic Worksheet With Answers Page 11
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22Ex: Construct a truth table for the following statement:
a. I study hard and ace the final, or I fail the course.
b. Suppose that you study hard, you do not ace the final and you fail the course. Under these
conditions, is this compound statement true or false?
First we represent our statements as follows:
p: I study hard.
q: I ace the final.
r: I fail the course.
Then we write the statement “I study hard and ace the final, or I fail the course” in symbolic
form:
.
Third, we build the table with three entries (p, q and r):
p
q
r
p
q
(p
q)
r
T
T
T
T
T
T
T
F
T
T
T
F
T
F
T
T
F
F
F
F
F
T
T
F
T
F
T
F
F
F
F
F
T
F
T
F
F
F
F
F
For part b, we have that p is True, q is false and r is true, which means we need to look on the
row #3. The conclusion is T, so that, under these conditions, the statement is True.
Not all the time we need to construct the truth table. We can determine the truth value of a
compound statement for a specific case in which the truth values of the simple statements are
known substituting the truth values of the simple statements into the symbolic form of the
compound statement and use the appropriate definitions to determine the truth value of the
compound statement.
Ex: On the previous example, part b, we set the truth values: p is True, q is false and r is true. So,
the statement
has in fact the value
.
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