Construct a truth table for p<-->(q V not p)
To construct a truth table for the given statement "p<-->(q V ¬p)", we need to consider all possible combinations of truth values for the variables p and q.
First, let's start by listing all the possible values for p and q:
p | q
------
0 | 0
0 | 1
1 | 0
1 | 1
Next, we need to evaluate the expression "q V ¬p" for each combination of p and q. The symbol "V" represents the logical OR operator, and "¬" represents the negation or logical NOT operator.
To find the value of "¬p", we simply negate the value of p. So, if p is 1, then ¬p will be 0, and vice versa.
Now, let's build the truth table step by step:
Step 1: Evaluate "¬p"
p | ¬p
-------
0 | 1
0 | 1
1 | 0
1 | 0
Step 2: Evaluate "q V ¬p"
p | q | ¬p | q V ¬p
-------------------
0 | 0 | 1 | 1
0 | 1 | 1 | 1
1 | 0 | 0 | 0
1 | 1 | 0 | 1
Finally, we evaluate the expression "p<-->(q V ¬p)", where "<-->" represents the logical biconditional operator. The biconditional operator is true when both sides have the same truth value, and false otherwise.
Step 3: Evaluate "p<-->(q V ¬p)"
p | q | ¬p | q V ¬p | p<-->(q V ¬p)
---------------------------------
0 | 0 | 1 | 1 | 1
0 | 1 | 1 | 1 | 0
1 | 0 | 0 | 0 | 0
1 | 1 | 0 | 1 | 1
So, the truth table for the given statement "p<-->(q V ¬p)" is as follows:
p | q | p<-->(q V ¬p)
--------------------
0 | 0 | 1
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1
This truth table represents all possible combinations of truth values for p and q and shows the resulting truth values for the expression "p<-->(q V ¬p)".