Construct a truth table for ~q (p q)
___p_|_t_|_f_| q__t_|_t_|_t_| ___f_|_t_|_f_|
"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.
p-4
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:)
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)
Making a truth table is actually very simple.For the statement P, it can either be true, or false.P--TFNOT P, or -p (or ~p) is the opposite. If P is true, then not P is... false!The same holds true for if P is false, what is not P? True!The truth table for ~p looks like thisP | ~p--------T | FF | T
___p_|_t_|_f_| q__t_|_t_|_t_| ___f_|_t_|_f_|
what is the correct truth table for p V~ q
truth table gives relation between i/p & o/p. excitation table is use for design of ff & counters.
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
A+
. p . . . . . q. 0 . . . . . 1. 1 . . . . . 0
I guess you mean q → p (as in the logic operator: q implies p).To create this truth table, you run over all truth values for q and p (that is whether each statement is True or False) and calculate the value of the operator. You can use True/False, T/F, 1/0, √/X, etc as long as you are consistent for the symbol used for True and the symbol used for False (the first 3 suggestions given are the usual ones used).For implies:if you have a true statement, then it can only imply a true statement to be truebut a negative statement can imply either a true statement or a false one to be truegiving:. q . . p . q→p--------------. 0 . . 0 . . 1 .. 0 . . 1 . . 1 .. 1 . . 0 . . 0 .. 1 . . 1 . . 1 .
1)p->q 2)not p or q 3)p 4)not p and p or q 5)contrudiction or q 6)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
P Q (/P or /Q) T T F T F T F T T F F T
P . . Q . . (P or Q)0 . . 0 . . . 00 . . 1 . . . 11 . . 0 . . . 11 . . 1 . . . 1=================P . . Q . . NOT(P and Q)0 . . 0 . . . . 10 . . 1 . . . . 11 . . 0 . . . . 11 . . 1 . . . . 0