Logic problems

May 2010
2
0
Hello there!
I have 3 tasks to solve, and I believe that I've achieved correct answer, but I might be totally wrong.

The question is if these expressions are correct or incorrect (true/false)

a) C -> (A -> B) |= -C ^ (-A v B)

b) C -> A( -> B) |= -C v -A v B

c) -C v (-A v B) |= C->(A->B)


I'd appreciate your help, and solutions for these tasks.

/David.T
 

emakarov

MHF Hall of Honor
Oct 2009
5,577
2,017
Recall that -A \/ B is equivalent to A -> B and try rewriting the formulas you are given using this equivalence as much as possible.
 
May 2010
2
0
for task a)
A = 1, B = 1, C = 1

LEFT: 1 -> (1 -> 1) gives 1 -> 1 gives 1

RIGHT: 0 ^ (0 v 1) gives 0 ^ 1 gives 0

1 =| 0 must be incorrect/false?
 
Dec 2008
288
13
do you not have any proof methods e.g semantic tableau that you can use?
 

emakarov

MHF Hall of Honor
Oct 2009
5,577
2,017
for task a)
A = 1, B = 1, C = 1

LEFT: 1 -> (1 -> 1) gives 1 -> 1 gives 1

RIGHT: 0 ^ (0 v 1) gives 0 ^ 1 gives 0

1 |= 0 must be incorrect/false?
Yes.
 
Dec 2008
288
13
can we not just simply draw up three tableau's for these to show if they are true or if not find a model using the tableau?