I know that two if-then statements are equivalent
I also know that an
if-then statement and its
are equivalent. So to fill in the blank of the first
column, I need to look for its
truth value in the contrapositive column. From
the table, it can be seen that in the contrapositive column the third row has a truth value of
therefore the missing truth value of the first column should be
also. And then, I also know that the converse and
of an if-
then statement are equivalent. Thus, to find the missing truth values of the converse and
inverse. I just have to
columns. Following this concept, I finally found out that
the missing truth values for the converse column are
while on the inverse column the missing truth values are
andT
and
F
corresponding
T T
contrapositive
inverse
compare the corresponding truth values of the converse and inverse
if their corresponding truth values are the same
I also know that an
if-then statement and its
are equivalent. So to fill in the blank of the first
column, I need to look for its
truth value in the contrapositive column. From
the table, it can be seen that in the contrapositive column the third row has a truth value of
therefore the missing truth value of the first column should be
also. And then, I also know that the converse and
of an if-
then statement are equivalent. Thus, to find the missing truth values of the converse and
inverse. I just have to
columns. Following this concept, I finally found out that
the missing truth values for the converse column are
while on the inverse column the missing truth values are
andT
and
F
corresponding
T T
contrapositive
inverse
compare the corresponding truth values of the converse and inverse
if their corresponding truth values are the same
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Answer:
A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results of the logical operation that the table represents (for example, P XOR Q). Each row of the truth table contains one possible configuration of the input variables (for instance, P=true Q=false), and the result of the operation for those values. See the examples below for further clarification. Ludwig Wittgenstein is generally credited with inventing and popularizing the truth table in his Tractatus Logico-Philosophicus, which was completed in 1918 and published in 1921.
1. If their corresponding truth values are the same
2.
3. Corresponding
4. F
5. F
6. Inverse
7. Compare the corresponding truth values of the converse and inverse.
8.F
9.T
10. F