0
What else can I help you with?
How can the statement "p implies q" be expressed in an equivalent form using the logical operator "or" and the negation of "p"?
The statement "p implies q" can be expressed as "not p or q" using the logical operator "or" and the negation of "p".
What is the relationship between p and q in the statement "p implies q"?
In the statement "p implies q," the relationship between p and q is that if p is true, then q must also be true.
What conditions must be met for the statement "p if and only if q" to be true?
The statement "p if and only if q" is true when both p and q are true, or when both p and q are false.
If not p, then not q?
If not p, then not q means that if something is not true or does not happen (p), then something else is also not true or does not happen (q).
What is modus ponens?
Modus Ponens is very simple. lets say you have this example If today is Monday, then tomorrow is Tuesday. Today is Monday Therefore tomorrow is Tuesday. That is a valid argument because of modus ponens If the premise(if today is monday) is true then you must accept the conclusion(Then Tommorow is Tuesday) as true also. Another example If P, then Q P Therefore Q
Which statement always has the same truth value as the conditional?
The statement "if not p, then not q" always has the same truth value as the conditional "if p, then q." They are logically equivalent.
P-q and q-p are logically equivalent prove?
p --> q and q --> p are not equivalent p --> q and q --> (not)p are equivalent The truth table shows this. pq p --> q q -->(not)p f f t t f t t t t f f f t t t t
How can the statement "p implies q" be expressed in an equivalent form using the logical operator "or" and the negation of "p"?
The statement "p implies q" can be expressed as "not p or q" using the logical operator "or" and the negation of "p".
If p q and q r then p r. Converse statement B.A syllogism C.Contrapositive statement D.Inverse statement?
Converse: If p r then p q and q rContrapositive: If not p r then not (p q and q r) = If not p r then not p q or not q r Inverse: If not p q and q r then not p r = If not p q or not q r then not p r
What is logically quivalent to q -- p?
It is: q+p because a double minus becomes a plus
What is the relationship between p and q in the statement "p implies q"?
In the statement "p implies q," the relationship between p and q is that if p is true, then q must also be true.
What does the statement p arrow q mean?
It means the statement P implies Q.
What is a contra positive statement?
Conditional statements are also called "if-then" statements.One example: "If it snows, then they cancel school."The converse of that statement is "If they cancel school, then it snows."The inverse of that statement is "If it does not snow, then they do not cancel school.The contrapositive combines the two: "If they do not cancel school, then it does not snow."In mathematics:Statement: If p, then q.Converse: If q, then p.Inverse: If not p, then not q.Contrapositive: If not q, then not p.If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true.
What conditions must be met for the statement "p if and only if q" to be true?
The statement "p if and only if q" is true when both p and q are true, or when both p and q are false.
What notation does a condition statement use?
"if p then q" is denoted as p → q. ~p denotes negation of p. So inverse of above statement is ~p → ~q, and contrapositive is ~q →~p. ˄ denotes 'and' ˅ denotes 'or'
What is converse inverse and contrapositive?
if the statement is : if p then q converse: if q then p inverse: if not p then not q contrapositive: if not q then not
What are conditional connectives. Explain use of conditional connectives with an example?
Conditional ConnectivesThe statement `if p then q' is called a conditional statement and is written logically as p ! q.(This asserts that the truth of p guarantees the truth of q.)p ! q can also be read as `p implies q', where p is sometimes called the antecedent and qtheconsequent.Examples:p: It is raining.q: I get wet.p ! q: If it is raining, then I get wet.s: It is Sunday.w: I have to work today.s ! w: If it is Sunday, then I have to work today.»s ! w: If it is not Sunday, then I have to work today.s !»w: If it is Sunday, I do not have to work today.(s ^ p) !»w: If it is Sunday and it's raining, then I don't have to work today.To examine the truth or falsity of p ! q, suppose p and q are the following propositionsp: I win the lottery,q: I will buy you a car.Then p ! q is the statement `If I win the lottery, then I will buy you a car'.
