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Nevermind you have give a direction in which it will be easier for me to proceed now on.
Do you have any idea about what are these {1}, {3} and {1,3} used in the above problem?
does T means syllogism?
Thank you for the explanation.
Why are these {1}, {3} and {1,3} used in the above problem?
Does T means Tautology? I know that CP means Conditional Proof.
If the question is itself half? Please let me know.
Does T, (2), (3) in last step means that Rule T is applied to Step number 2 and 3?
Hello Guys,
I don't require a stepwize solution for this problem? I just want to know what is rule P and T in Predicate Calculus.
The Question is as follows. I am even writing in the Answer. Please explain me what it is.
Topic:- Discrete Mathematics.
Question:- In Theory of Inference for the Predicate Calculus the Method of Derivation of Predicate forumlas uses the rules P and T. What are these Rules P and T?
Problem: - Show that (x) (H(x)->M(x)) n H(s) <-> M(s). This Problem is a symbolic Translation of a well-known argument known as "socrates argument" which is given by:
All men are mortal.
Socrates is a man.
Therefore Socrates is a mortal.
If we deonte H(x): x is a man, M(x): x is a mortal, and s: Socrates, we can put the argument in the form.
Solution:-
{1} (1) (x) (H(x)->M(x)) P------- What is P in this step? What is {1} in this step?
{1} (2) H(s)->M(s) US, (1) ------- What is US, (1) in this step?
{3} (3) H(s) P ------- Again what is P in this step? Why {3} is used in this step and not {1}?
{1,3} (4) M(s) T, (2), (3) ------- why {1,3} is used in this step and what does T, (2), (3) means?
Is {1}, {3} and {1,3} the Universe of Discourse?
regards,
rocky sheedy.
I was doing 10 different things at a time due to which I was not able to give proper attention to two of the problem. I did not had time to solve it. I wanted it for one day. Now, there is no need for the solution of this one. Now I have ample of time to understand the concept behind. The book that I was refering to was itself in shortcut and with some typos due to which it was becoming tedious to analyze and dissect that rubbish book.
If incase I stuck up in that I will let you know.
Thanks a lot.
I did not had time to solve it. I wanted it for one day. Now, there is no need for the solution of this one. Now I have ample of time to understand the concept behind.
If incase I stuck up in that I will let you know.
Thanks a lot.
How many 5 symbol codes can be formed if first 2 are letters and next 3 are digits?
Topic: - Discrete Mathematics
How many 5-symbol codes can be formed if the first 2 symbols are letters and next 3 are digits but no symbol is repeated?
If possible Please write in the Entire Step by Step answer.
Set of all straight lines under the relation is parallel to is an equivalence relation?
Topic:- Discrete Mathematics
Verify that the set of all straight lines under the relation is parallel to is an equivalence relation?
Does any one has the stepwise solution of this problem?
Question: - Consider the differential equation y" + Q(x)y = 0 where Q(x) is continuous on [a,b]. If Qm is the minimum value of Q(x) on [a,b] and Qm is greater than [k square pie square/ square of (b-a)] show that non trivial solution of the differential equation has at least K zeros on [a,b].
Solution:- What is the solution for this problem.
Theorem:-
Let y1 and y2 be two solutions of the 2nd order Homogenous Linear differential equation y" + P(x)y' + Q(x)y = 0 on [a,b]. Show that y1 and y2 are Linearly dependant if and only if Wronskian is identically zero [a, b].
Proof:- How to prove this theorem. Please post the proof if you have any for this theorem.
In Metric Space if d and d* are two Metrics.
If d*(x,y) <= d(x,y) then how {x belongs to X: d(p,x)<r} is the proper subset of {x belongs to X: d*(p,x)<r}. Is is correct? If yes could you please explain?
Shouldn't it be ---------------
If d*(x,y) <= d(x,y) then {x belongs to X: d*(p,x)<r} is the proper subset of {x belongs to X: d(p,x)<r}.
The exact question and solution is as follows:
Question:- Let (X,d) be a Metric Space and let d*(x,y) = min {1,d(x,y)}. Even d* is a Metric. Show that d and d* are equivalent?
Solution:- Inorder to prove d and d* are equivalent it suffices to show that d-open sphere about a point p belongs to X contains a d*-open sphere about p and conversely.
Since d*(x,y) <= d(x,y) we have {x belongs to X: d(p,x)<r} is the proper subset of {x belongs to X: d*(p,x)<r}. -------------------->This is where I am stucked how is it possible. How can {x belongs to X: d*(p,x)<r} be bigger than {x belongs to X: d(p,x)<r} when d*(x,y) is smaller or equal to d(x,y).
for every p belongs to X and every r > 0. On the other hand, if r is any positive number, let
q=min(r,1). Then {x belongs to X: d*(p,x)<q} is the proper subset of {x belongs to X: d(p,x)<q}
For every p belongs to X.
It follows that d-open set is a d*-open and every d*-open set is d-open. Hence both are equivalent.
Thank you for your reply.
I would like to know how exactly the placing takes place. Correct me if I am wrong.
Now the word 'FATE' has four letters F, A, T, E..........
We have to approach as per alphabetical manner like A, E, F, T.
Then for A there are 6 permutations and for E there are 6 permutation.
Now coming to F:- If F is the first letter of of the word there are remaining 3 places for remaining 3 letters that is for A, E, T now even these letters should be taken in alphabetical order.......like.....A, E and then T. So we get first two positions occupied by F and A and hence the word is.........FA
Now there are remaining 2 places for remaining 2 letters that is for E, T again take alphabet which is comes first for e.g. E comes before T hence take E. Now the arrangement becomes....FAE
Now place the last letter T in the last place and so the word becomes....... FAET-----------1
Now we have found out one permutation starting from F
To find another arrangements starting from letter F and second postion occupied by A so there are remaining 2nd positions for remaining 2 letters E and T. We have already found out the arrangement by fixing E in the 3rd position hence this time we place T in the 3rd position and place E in the 4th position The word that we get is.............FATE----------------------2
Now we have reached to the main word arrangement that is FATE hence we stop here as we were asked to find the rank of the word FATE otherwise we could have proceeded further by fixing E in the 2nd position and then putting A in the 3rd position and then T in the 4th position.
Then again fixing E in the 2nd position and interchanging the postion of A and T....
Then again fixing T in the first position and so on............... If we had to find out the rank of the word which would have started from T in this case.
I apologize for prompting. Does this comes under Permutation(Arrangements) or Combinations because you have mentioned about the combination. I might be wrong.
regards,
rocky sheedy.
Hello,
Here is a permutation question to find the rank of the word FATE:
Question:- If the letters of the word 'FATE' are arranged as in a dictionary, what is the rank of the word?
Solution:- The alphabetical order of the letter is A, E, F, T. The number of arrangements begining with A is got by putting A in the first place and arranging the other 3 letters. This can be done in 3 factorial ways.
Therefore the Number of arrangements which begin with A = 3 Factorial = 6
Therefore the Number of arrangements which begin with E = 3 Factorial = 6
The next arrangement is FAET = 1
The next arrangement is FATE = 1 --------------------- --------------- Why not the number of arrangement which begins with F is 3 factorial? Why only two arrangements starting with F are considered? There can be even other arrangement of the word FATE starting from F... like FTAE, FTEA, FEAT, FETA........why even these arrangements are not taken
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