827.sagews

(A ^ B') ->(A->B)'

Connective is -> IMPLICATION so Statement must be either TRUE->TRUE or FALSE->FALSE to be a Tautology.

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

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

We see only TRUE & FALSE = TRUE.

Now lets simplify the other side of the connective. we now know we need TRUE -> TRUE = TAUTOLOGY

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

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

We need TRUE->FALSE = 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 True True True False

Now A or B can become TRUE

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

A value False True True True

Or

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

B value False True True True