List of top Mathematics Questions on Mathematical Logic

Consider the following logical statements:
R: If \(p \rightarrow q\) is false, then \(p \vee q\) is false.
S: If \(p \leftrightarrow q\) is false, then \(p \vee q\) is false.
Evaluate the truth values of R and S.

The number of ordered triplets of the truth values of \( p, q, r \) and such that the truth value of the statement \[ (p \lor q) \land (p \lor r) \implies (q \lor r) \text{ is True, is equal to:} \]

The negation of the compound proposition $p \vee (\neg p \vee q)$ is

The statement $P(n) = 9^{n} - 8^{n}$, when divided by 8, always leaves the remainder

If $P(n): 1 + 3 + 5 + \cdots + (2n-1) = n^2$ is

The equation of the circle circumscribing the triangle formed by the lines $x+y=6$, $2x+y=4$ and $x+2y=5$ is

Negation of "Paris is in France and London is in England" is

If $P(n)$ is a statement such that $P(3)$ is true. Assuming $P(k)$ is true $\Rightarrow P(k+1)$ is true for all $k \ge 3$, then $P(n)$ is true

$(p \land q) \lor (\sim p \land \sim q)$ is