Is true when both p and q are true and is false otherwise?
The proposition “p and q,” denoted by pq is true when both p and q are true and is false otherwise. This is called the conjunction of p and q. Let p and q be propositions. The proposition “p or q,” denoted by pq, is the proposition that is false when p and q are both false and true otherwise.
When P is true and Q is false then PQ?
If p and q are propositions, the conditional “if p then q” (or “p only if q” or “q if p), denoted by p → q, is false when p is true and q is false; otherwise it is true. p is a sufficient condition for q and q is a necessary condition for p. The contrapositive of a conditional statement of p → q is ¬q → ¬p.
When P is false and Q is false?
In the truth tables above, there is only one case where “if P, then Q” is false: namely, P is true and Q is false….IF…., THEN….
| P | Q | If P, then Q |
|---|---|---|
| F | F | T |
What is the truth value when p is true and q is false?
If p=T, then we must have ~p=F. Now that we’ve done ~p, we can combine its truth value with q’s truth value to find the truth value of ~p∧q. (Remember than an “and” statment is true only when both statement on either side of it are true.)…Truth Tables.
| p | q | p∧q |
|---|---|---|
| T | F | F |
| F | T | F |
| F | F | F |
Is P Q true?
The proposition p is called hypothesis or antecedent, and the proposition q is the conclusion or consequent. Note that p → q is true always except when p is true and q is false.
Is p or q false?
Conditional Propositions – A statement that proposes something is true on the condition that something else is true. For example, “If p then q”* , where p is the hypothesis (antecedent) and q is the conclusion (consequent). This Disjunction is False because both propositions are false.
When p is false and q is true then p or q is true quizlet?
The conditional statement p → q is the proposition “if p, then q.” The conditional statement p → q is false when p is true and q is false, and true otherwise. In the conditional statement p → q, p is called the hypothesis (or antecedent or premise) and q is called the conclusion (or consequence).
Is PQ True or false?
The conditional of q by p is “If p then q” or “p implies q” and is denoted by p q. It is false when p is true and q is false; otherwise it is true. A conditional statement is logically equivalent to its contrapositive.
Where p and q are statements p q is called the?
A statement (or proposition) is a sentence that is true or false but not both. Given another statement q, the sentence “p ∧ q” is read “p and q” and is called the conjunction of p and q.
Where p and q are statements p and q is false if/p is false?
If p and q are statement variables, the conjunction of p and q is “p and q,” denoted p ∧ q. It is true when, and only when, both p and q are true. If either p or q is false, or if both are false, p ∧ q is false.