If p → ( ¬p ∨ q) is false, then the truth values of p and q are respectively T, F.Group startsTrue or FalseTrue, unselectedFalse, unselected
Question
If p → ( ¬p ∨ q) is false, then the truth values of p and q are respectively T, F.Group startsTrue or FalseTrue, unselectedFalse, unselected
Solution
To determine the truth values of p and q in the given statement, let's analyze the expression p → (¬p ∨ q) when it is false.
-
The expression p → (¬p ∨ q) is false when the antecedent (p) is true and the consequent (¬p ∨ q) is false.
-
Since the antecedent (p) is true, we can conclude that p is true.
-
Now, let's analyze the consequent (¬p ∨ q). Since the entire expression is false, the consequent must also be false.
-
The expression ¬p ∨ q is false when both ¬p and q are false.
-
Since the consequent (¬p ∨ q) is false, we can conclude that both ¬p and q are false.
Therefore, the truth values of p and q in the given statement are p = true and q = false.
Similar Questions
The proposition p↔q is equivalent to (¬p ∨ q) ∧(¬q ∨ p) Group startsTrue or FalseTrue, unselectedFalse
The negation of (P ∧ q) → r is P ∧ q ∧ ¬ rGroup startsTrue or FalseTrue, unselectedFalse
This statement: [(p → q) ↔ (¬ p ∨ q) ] is tautologyGroup startsTrue or False
If p is false and q is true, what is the truth value of (p∧q)∨q?truefalsecannot be determinedSubmit
If p is False and q is True, what is the truth value of ~p <--> ~qGroup of answer choicesTrueFalse
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.