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) Make a truth table for the propositional statement P (grp) ^ (¬(p→ q))

User Nirpi
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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.

User Nicolas Bonnet
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