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"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.
What else can I help you with?
What equals twice the difference of p and q?
The difference of p and q can be written : p - q Twice the difference is therefore 2 x (p - q) which can also be written as 2(p - q) OR 2p - 2q. Consequently you can create another variable (say) y and make this equal to twice the difference of p and q by simply writing, y = 2(p -q)
What does p over q mean in algebra?
P! / q!(p-q)!
If B is between P and Q?
If B is between P and Q, then: P<B<Q
What is 4 times the sum of q and p?
4(p + q), or 4p + 4q
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 friendship?
Not exactly sure what you're talking about, but this is an example of proofs: 1. If P, then Q 2. P/Not P 3. Therefore Q/ Not Q For example, 1. If I have whiskers, then I am a cat 2. I have whiskers 3. Therefore I am a cat
What is the proof of the modus ponens not by the truth table?
1)p->q 2)not p or q 3)p 4)not p and p or q 5)contrudiction or q 6)q
What the answer If p then q Not q Therefore not p modus tollens or what?
The argument "If p then q; Not q; Therefore not p" is an example of modus tollens. Modus tollens is a valid form of reasoning that states if the first statement (p) implies the second statement (q) and the second statement is false (not q), then the first statement must also be false (not p).
Is not(p and q) equal to (not p) or q?
No, the statement "not(p and q)" is not equal to "(not p) or q." According to De Morgan's laws, "not(p and q)" is equivalent to "not p or not q." This means that if either p is false or q is false (or both), the expression "not(p and q)" will be true. Therefore, the two expressions represent different logical conditions.
Which term best describes the statement if p q and q r the p r?
The statement "if p, then q; and if q, then r; therefore, if p, then r" describes the logical reasoning known as the transitive property. More formally, it can be expressed in symbolic logic as "p → q, q → r, therefore p → r." This is a fundamental concept in logic that illustrates how relationships can be inferred through a chain of implications.
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).
How does every rational number have an additive inverse?
By definition, every rational number x can be expressed as a ratio p/q where p and q are integers and q is not zero. Consider -p/q. Then by the properties of integers, -p is an integer and is the additive inverse of p. Therefore p + (-p) = 0Then p/q + (-p/q) = [p + (-p)] /q = 0/q.Also, -p/q is a ratio of two integers, with q non-zero and so -p/q is also a rational number. That is, -p/q is the additive inverse of x, expressed as a ratio.
If P 50 of Q and Q 50 of R then P Q R?
If P is 50% of Q, this means that P is half the value of Q. Similarly, if Q is 50% of R, then Q is half the value of R. Therefore, P is 25% of R, as it is 50% of Q, which is itself 50% of R. Thus, we can conclude that P is less than both Q and R.
What equals twice the difference of p and q?
The difference of p and q can be written : p - q Twice the difference is therefore 2 x (p - q) which can also be written as 2(p - q) OR 2p - 2q. Consequently you can create another variable (say) y and make this equal to twice the difference of p and q by simply writing, y = 2(p -q)
A trait has 2 alleles represented by p and q. If p 0.35 what is q?
In a trait with two alleles represented by p and q, the sum of the frequencies of the alleles must equal 1. Therefore, if p = 0.35, you can find q by subtracting p from 1. This gives q = 1 - 0.35, which means q = 0.65.
If p equals 0.35 what is q?
In probability theory, if ( p ) represents the probability of an event occurring, then ( q ) is typically defined as the probability of the event not occurring. Therefore, if ( p = 0.35 ), you can calculate ( q ) using the formula ( q = 1 - p ). Thus, ( q = 1 - 0.35 = 0.65 ).
What is the demand elasticity of P 100-4Q when Q 20?
The quantity, Q, demanded at price P is 100 - 4Q So Q = 25 - P/4 And therefore, the demand elasticity is -1/4 or -0.25, whatever the value of Q.
