"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.
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)
P! / q!(p-q)!
If B is between P and Q, then: P<B<Q
4(p + q), or 4p + 4q
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)
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
1)p->q 2)not p or q 3)p 4)not p and p or q 5)contrudiction or q 6)q
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).
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.
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)
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.
If 59 out of 100 organisms are P, then the remaining organisms would be Q. Therefore, Q would be 41 out of 100 organisms.
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
The sum of p and q means (p+q). The difference of p and q means (p-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
q + p
0.65