Tagged Questions
1
vote
1answer
51 views
What does $\vdash s \rightarrow (\neg s\rightarrow t)$ mean?
What does this statement mean $\vdash s \rightarrow (\neg s\rightarrow t)$?
And how can I prove it?
0
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2answers
38 views
what is the diffrence between a term , constant and variable in first order logic languages ?
in the text , the author says that the language contains parenthises , sentintial connectives and n-place functions , n-place predicates , equality sign = , terms , constans and variables
i have two ...
-2
votes
1answer
44 views
How to prove that a set of connectives aren't adequate
I guess we have to prove it somehow by an induction as I saw a few examples online. But it just makes absolutely no sense to me... Can somebody explain it in human language? Thank you very much.
1
vote
1answer
34 views
Appearance of sentence parameters in a theorem
Is it true that if $A$ is a formula in a Hilbert system $H$, then if $B_1,B_2,\ldots,B_n$ is a proof of $A$ in $H$, any sentence parameter not appearing in $A$ doesn't appear in $B_1,\ldots,B_n$? If ...
3
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2answers
57 views
Is there a difference between 'inconsistent', 'contrary', and 'contradictory'
Is there a difference between 'inconsistent' 'contrary' and 'contradictory'? As far as I understand, two statements are inconsistent when they can not both be true; two statements are contradictory ...
1
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1answer
69 views
-7
votes
0answers
46 views
3
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0answers
36 views
Boolean combinatorics
Every finite Boolean algebra has a "middle layer", corresponding to the subsets of size $n/2$ (when looking at the algebra of subsets of $[n]$) or to a set of formulas including $p_i, \neg p_i, p_i ...
1
vote
2answers
87 views
Do the premises logically imply the conclusion?
$$b\rightarrow a,\lnot c\rightarrow\lnot a\models\lnot(b\land \lnot c)$$
I have generated an 8 row truth table, separating it into $b\rightarrow a$, $\lnot c\rightarrow\lnot a$ and $\lnot ...
1
vote
4answers
73 views
Writing an expression using logic
Write an expression using letters $\land, \lor, and$ $\neg$ which has the following truth table:
$$\begin{array}{ccc|c}
P&Q&R&???\\ \hline
T&T&T&F\\
T&T&F&T\\
...
0
votes
3answers
69 views
what is the relation between not A and everything but A
I am examining Bayes' Theorem, and wondering about the alternative interpretations of ~A, as being:
not A, ¬ A
everything but A, ∀-A
And how this will affect the use of probabilities.
...
2
votes
2answers
57 views
Are these propositions equivalent?
Statement 1: Maria will find job if she learns mathematics.
Statement 2: Maria will find a job unless she does not learn
mathematics.
I know the answer is probably that these are same, but ...
3
votes
1answer
34 views
Boolean Algebra Transform
I am revisiting Boolean algebra after a long while.
Can somebody help show me how to simplify the LHS to get the RHS?
$$abc * a'bc + (abc)' * (a'bc)'\quad = \quad \;b'+c'$$
2
votes
3answers
65 views
Logic Negation Symbols
This is a rather simple question but I can't find an exact answer on it...
In examples I've seen, i've seen the ~ symbol and the ¬ symbol. These fall under 'negation'. if they both fall under ...
1
vote
1answer
43 views
Simple logic equivalence incorrect
I am having some problems negating a rather simple logical statement. I am currently taking a introduction course, so please bear with me if my question is silly.
I am supposed to turn this:
$$ ...
