(pVq)--> ~p Construct a truth table
(xvy) -z
y/z
To construct a truth table for the given expression (pVq)--> ~p, we need to evaluate the expression for all possible combinations of truth values for the variables p and q.
First, let's list out all possible combinations of truth values for p and q. Since there are two variables, there are four possible combinations:
1. p = true, q = true
2. p = true, q = false
3. p = false, q = true
4. p = false, q = false
Now, let's evaluate the given expression (pVq)--> ~p for each of these combinations.
For combination 1 (p = true, q = true):
- (pVq) evaluates to true, as p or q has a truth value of true.
- ~p evaluates to false, since p is true.
- (pVq)--> ~p evaluates to false, since true implies false.
For combination 2 (p = true, q = false):
- (pVq) evaluates to true, as p or q has a truth value of true.
- ~p evaluates to false, since p is true.
- (pVq)--> ~p evaluates to false, since true implies false.
For combination 3 (p = false, q = true):
- (pVq) evaluates to true, as p or q has a truth value of true.
- ~p evaluates to true, since p is false.
- (pVq)--> ~p evaluates to true, since true implies true.
For combination 4 (p = false, q = false):
- (pVq) evaluates to false, as both p and q have a truth value of false.
- ~p evaluates to true, since p is false.
- (pVq)--> ~p evaluates to true, since false implies true.
Now, we can summarize these results in a truth table:
| p | q | (pVq) | ~p | (pVq)--> ~p |
|-----|-----|-------|-----|-------------|
| true | true | true | false | false |
| true | false | true | false | false |
| false | true | true | true | true |
| false | false | false | true | true |
This is the truth table for the expression (pVq)--> ~p. It shows the corresponding truth values for each combination of variables p and q.