List of top Mathematics Questions on Logic gates

The statement \( [(p \rightarrow q) \wedge \sim q] \rightarrow r \) is a tautology when \( r \) is equivalent to:
If \( p \land q \) is False and \( p \rightarrow q \) is False, then the truth values of \( p \) and \( q \) are:
If the statement \( p \leftrightarrow (q \rightarrow p) \) is false, then the true statement is:
Using the rules in logic, write the negation of the following: \[ (p q) \land (q \lor \sim r) \]

The negation of \( (p \land (\sim q)) \lor (\sim p) \) is equivalent to:

If p, q and r are three propositions, then which of the following combination of truth values of p, q and r makes the logical expression \({(p∨q)∧((∼p)∨r)}🡢((∼q)∨r)\) false?