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Law of detachment?
Law of Detachment also known as Modus Ponens (MP) says that if p=>q is true and p is true, then q must be true. The Law of Syllogism is also called the Law of Transitivity and states: if p=>q and q=>r are both true, then p=>r is true.
What is the Law of detachment?
AnswerLaw of Detachment ( also known as Modus Ponens (MP) ) says that if p=>q is true and p is true, then q must be true.example:If an angle is obtuse, then it cannot be acute.Angle A is obtuse.ThereforeAngle A cannot be acute.The Law of Syllogism ( also called the Law of Transitivity ) states:if p=>q and q=>r are both true, then p=>r is true.example:If the electric power is cut, then the refrigerator does not work.If the refrigerator does not work, then the food is spoiled.So if the electric power is cut, then the food is spoiled.Law of Detachment also known as Modus Ponens (MP) says that if p=>q is true and p is true, then q must be true.The Law of Syllogism is also called the Law of Transitivity and states: if p=>q and q=>r are both true, then p=>r is true.In a nutshell, it's saying that if you have a conditional, and you have the antecedent, you then have the consequent. For example, we know that, "If it snows this winter, we will need to wear warm winter clothing outside." Suddenly it's mid-December and the forecast is snow. Therefore, it's probably the time to go shopping for winter clothes, if we don't already have any.
If P is true and Q is false what is the truth value of P or Q?
If p is true and q is false, p or q would be true. I had a hard time with this too but truth tables help. When using P V Q aka p or q, all you need is for one of the answers to be true. Since p is true P V Q would also be true:)
Is not p and q equivalent to not p and not q?
Think of 'not' as being an inverse. Not 1 = 0. Not 0 = 1. Using boolean algebra we can look at your question. 'and' is a test. It wants to know if BOTH P and Q are the same and if they are 1 (true). If they are not the same, or they are both 0, then the result is false or 0. not P and Q is rewritten like so: (P and Q)' = X not P and not Q is rewritten like: P' and Q' = X (the apostrophe is used for not) We will construct a truth table for each and compare the output. If the output is the same, then you have found your equivalency. Otherwise, they are not equivalent. P and Q are the inputs and X is the output. P Q | X P Q | X ------ 0 0 | 1 0 0 | 1 0 1 | 1 0 1 | 0 1 0 | 1 1 0 | 0 1 1 | 0 1 1 | 0 Since the truth tables are not equal, not P and Q is not equivalent to not P and not Q. Perhaps you meant "Is NOT(P AND Q) equivalent to NOT(P) AND NOT(Q)?" NOT(P AND Q) can be thought of intuitively as "Not both P and Q." Which if you think about, you can see that it would be true if something were P but not Q, Q but not P, and neither P nor Q-- so long as they're not both true at the same time. Now, "NOT(P) AND NOT(Q)" is clearly _only_ true when BOTH P and Q are false. So there are cases where NOT(P AND Q) is true but NOT(P) AND NOT(Q) is false (an example would be True(P) and False(Q)). NOT(P AND Q) does have an equivalence however, according to De Morgan's Law. The NOT can be distributed, but in doing so we have to change the "AND" to an "OR". NOT(P AND Q) is equivalent to NOT(P) OR NOT(Q)
What is the proof for P and Not P Therefore Q?
"P and not P" is always false. If P is true, not P is false; if P is false, not P is true. In either case, combining a true and a false with the AND operator gives you false. And if you look at the truth table for the implication (the "therefore" part), when the left part is false, the result is always true.
Law of detachment?
Law of Detachment also known as Modus Ponens (MP) says that if p=>q is true and p is true, then q must be true. The Law of Syllogism is also called the Law of Transitivity and states: if p=>q and q=>r are both true, then p=>r is true.
What is the law f detachment?
Law of Detachment states if p→q is true and p is true, then q must be true. p→q p therefore, q Ex: If Charlie is a sophomore (p), then he takes Geometry(q). Charlie is a sophomore (p). Conclusion: Charlie takes Geometry(q).
What is the law of modus tollens?
It in Math, (Geometry) If p implies q is a true conditional statement and not q is true, then not p is true.
What is the truth table for p arrow q?
Not sure I can do a table here but: P True, Q True then P -> Q True P True, Q False then P -> Q False P False, Q True then P -> Q True P False, Q False then P -> Q True It is the same as not(P) OR Q
What is the Law of detachment?
AnswerLaw of Detachment ( also known as Modus Ponens (MP) ) says that if p=>q is true and p is true, then q must be true.example:If an angle is obtuse, then it cannot be acute.Angle A is obtuse.ThereforeAngle A cannot be acute.The Law of Syllogism ( also called the Law of Transitivity ) states:if p=>q and q=>r are both true, then p=>r is true.example:If the electric power is cut, then the refrigerator does not work.If the refrigerator does not work, then the food is spoiled.So if the electric power is cut, then the food is spoiled.Law of Detachment also known as Modus Ponens (MP) says that if p=>q is true and p is true, then q must be true.The Law of Syllogism is also called the Law of Transitivity and states: if p=>q and q=>r are both true, then p=>r is true.In a nutshell, it's saying that if you have a conditional, and you have the antecedent, you then have the consequent. For example, we know that, "If it snows this winter, we will need to wear warm winter clothing outside." Suddenly it's mid-December and the forecast is snow. Therefore, it's probably the time to go shopping for winter clothes, if we don't already have any.
Examples of deductive reasoning in geometry?
Law of Syllogism If p->q and q->r are true conditionals, then p -> r is also true. (P)If people live in Manhattan, (q) then they live in New York. (q)If people live in New York, (r) then they live in the United States. Law of Detachment IF p-> q is a true conditional and p is true, then q is true. If you break an item in a store, you must pay for it. (P) Jill broke a vase in Potter's Gift Shop. (q) Jill must pay for the vase.
What is the law of contrapositive?
If p->q, then the law of the contrapositive is that not q -> not p
If P is true and Q is false what is the truth value of P or Q?
If p is true and q is false, p or q would be true. I had a hard time with this too but truth tables help. When using P V Q aka p or q, all you need is for one of the answers to be true. Since p is true P V Q would also be true:)
What is a comparative operator?
Comparative operators are used to compare the logical value of one object with another and thus establish the rank (ordering) of those objects. There are six comparative operators in total: p<q : evaluates true when p is less than q p>q : evaluates true when p is greater than q p<=q : evaluates true when p is less than or equal to q p>=q : evaluates true when p is greater than or equal to q p!=q : evaluates true when p is not equal to q p==q : evaluates true when p is equal to q
How do you construct a truth table for parenthesis not p q parenthesis if and only if p?
Assuming that you mean not (p or q) if and only if P ~(PVQ)--> P so now construct a truth table, (just place it vertical since i cannot place it vertical through here.) P True True False False Q True False True False (PVQ) True True True False ~(PVQ) False False False True ~(PVQ)-->P True True True False if it's ~(P^Q) -->P then it's, P True True False False Q True False True False (P^Q) True False False False ~(P^Q) False True True True ~(P^Q)-->P True True False False
If p is true and q is false what is the truth value or p or q?
true or false = true
What do you know to be true about the values of p and q?
p = q
