Answer:
To make a truth table for the propositional statement P (grp) ^ (¬(p→ q)), we need to list all possible combinations of truth values for the propositional variables p, q, and P (grp), and then evaluate the truth value of the statement for each combination. Here's the truth table:
| p | q | P (grp) | p → q | ¬(p → q) | P (grp) ^ (¬(p → q)) |
|------|------|---------|-------|----------|-----------------------|
| true | true | true | true | false | false |
| true | true | false | true | false | false |
| true | false| true | false | true | true |
| true | false| false | false | true | false |
| false| true | true | true | false | false |
| false| true | false | true | false | false |
| false| false| true | true | false | false |
| false| false| false | true | false | false |
In this truth table, the column labeled "P (grp) ^ (¬(p → q))" shows the truth value of the propositional statement for each combination of truth values for the propositional variables. As we can see, the statement is true only when P (grp) is true and p → q is false, which occurs when p is true and q is false.