29B-TautologyTest

150 days ago by pytheas_fogg

[(A->B)^A] ->B

B is TRUE so we want to verify the other side of the connective is also true.

import sage.logic.propcalc as propcalc One = propcalc.formula("(A->B)"); One.truthtable();

A      B      value
False  False  True   
False  True   True   
True   False  False  
True   True   True

We see TRUE -> TRUE = TRUE

import sage.logic.propcalc as propcalc One = propcalc.formula("(B & A)"); One.truthtable();

B      A      value
False  False  False  
False  True   False  
True   False  False  
True   True   True

We see TRUE & TRUE = TRUE

import sage.logic.propcalc as propcalc One = propcalc.formula("(B -> B)"); One.truthtable();

B      value
False  True   
True   True

TRUE -> TRUE = TAUTOLOGY