Table of Contents
What is the truth value of p/if p is true?
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 |
When both P and q are true?
Conjunction – an “and” statement. Given two propositions, p and q, “p and q” forms a conjunction. The conjunction “p and q” is only true if both p and q are true.
Is P ∨ q true?
The truth or falsehood of a proposition is called its truth value. Note that ∨ represents a non-exclusive or, i.e., p ∨ q is true when any of p, q is true and also when both are true. On the other hand ⊕ represents an exclusive or, i.e., p ⊕ q is true only when exactly one of p and q is true. 1.1.
Which is the inverse of P → Q?
Suppose a conditional statement of the form “If p then q” is given. The inverse is “If ~p then ~q.” Symbolically, the inverse of p q is ~p ~q.
When P is false and q is true?
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 |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
What is the proposition that is true when exactly one of p and q is true and is false otherwise?
The exclusive or of p and q, denoted by pq, is the proposition that is true when exactly one of p and q is true and is false otherwise.
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).
What is the value of true if and only if true?
It says that P and Q have the same truth values; when “P if and only if Q” is true, it is often said that P and Q are logically equivalent. In fact, when “P if and only Q” is true, P can subsitute for Q and Q can subsitute for P in other compound sentences without changing the truth….IF AND ONLY IF.
| P | Q | P if and only if Q |
|---|---|---|
| F | T | F |
| F | F | T |
What is the truth value of the conditional statement when the hypothesis is true and the conclusion is false?
If the hypothesis is true and the conclusion is true, the conditional statement if p, then q is true. If the hypothesis is true but the conclusion is false, the statement is false.
When p is false and q is true then p or q is?
What is P and q in math?
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.
What does P and q stand for in math?
In conditional statements, “If p then q” is denoted symbolically by “p q”; p is called the hypothesis and q is called the conclusion. For instance, consider the two following statements: If Sally passes the exam, then she will get the job. If 144 is divisible by 12, 144 is divisible by 3.