Question

Find all combinations of truth values for p, q and r for which the statement ¬p ↔ (q ∧ ¬(p → r)) is true

Answer 1

Let's compose a truth table:

Then  the statement ¬p ↔ (q ∧ ¬(p → r)) is true if$\left( {p = True,\,\,q = r = False} \right);\,\,\,\left( {p = r = True,q = False} \right);\,\,\left( {p = q = r = True} \right)$

Answer: $\left( {p = True,\,\,q = r = False} \right);\,\,\,\left( {p = r = True,q = False} \right);\,\,\left( {p = q = r = True} \right)$