Recent content by wololo

The thing is, I was never wrong, since the last column in the truth table is NOT a vacuous truth...

I agree that P->Q is only false when P is true and Q is false. If P is false, whatever value Q, P->Q will be true, so we both agree on that. The thing is that my truth table is not for an implication, but for an equivalence between an implication and an atom. Suppose we use a simple statement...

Yeah but the statement the person said P→(¬P∨¬Q∨¬R) will always be TRUE if he is a knight and always FALSE if he is a knave. This is why I added an if and only if in front of it. P⟺P→(¬P∨¬Q∨¬R) then means (if i am a knight, then at least on of us is a knave) is only true when the person...

Homework Statement A person can either be a knight (always tells the truth) or a knave (always tells a lie). On an island with three persons (A, B and C), A tells "If I am a knight, then at least one of us is a knave". Homework Equations Truth tables, logic rules. The Attempt at a Solution...

I think all the edges that are not in a maximum spanning tree wil give me the minimum hitting set.

Could I simply use Boruvka's algorithm to get a minimum spanning tree and add these edges to F?

Homework Statement Homework Equations Recursion, graphs, DFS The Attempt at a Solution To try to solve this algorithm, I first need to find all the basic cycles in the Graph G. When I have these cycles, I can simply pick the smallest edge in each of them and add them to the set F, while...

"The player who removes the last match wins, except if there is only one match left, in which case the game is a draw." All the paths that end in 1 in the game tree are draws.

Homework Statement Homework Equations Tree data structures. I think it might also have something to do with minimax algorithm, but it was only mentioned once and never discussed extensively in class so I doubt it is required. The Attempt at a Solution [/B] If both players play as well as...

Homework Statement Homework Equations Maxwell relations The Attempt at a Solution Here is how I proceeded. Am I allowed to go from line 1 to 2? It almost seems too simple. dU=TdS-PdV \\ (\frac{\partial U}{\partial P})_T=T(\frac{\partial S}{\partial P})_T-P(\frac{\partial V}{\partial P})_T...

If I rewrite the expression for T and isolate S i get S=(27T^3V)/(64A). I can then replace the integral of -SdT to find F by the integral of -(27T^3V)/(64A)dT which equals -(27T^4V)/(256A). It seems to make sense since I get rid of the S terms in the first integral. However I don't see how I...

I still haven't figured out how to get rid of the entropy terms in the expression of Helmholtz free energy. Can I simply replace the S in the equation I found by heat capacity times temperature? (given dS=cdT). I don't know how to proceed after, any advice is appreciated. Am I on the correct...

Homework Statement Homework Equations Maxwell relations The Attempt at a Solution I have an attempt at a solution, but I am not sure if I can replace the integral of dT in the helmholtz equation by the T I found using the internal energy. Does this make sense? Thanks

Homework Statement Homework Equations Chain rule, partial derivation The Attempt at a Solution dv/dt=dv/dx*dx/dt+dv/dy*dy/dt dx/dt=-4t -> evaluate at (1,1) =-4 dv/dt=-4dv/dx+4(-2) dv/dt=-4dv/dx-8 How can I find the missing dv/dx in order to get a value for dv/dt? Thanks!

Oh I see I was only checking at (0,0) not for (xi, 0) (0, yi). Thanks!