The number of values of $r \in\{p, q, \sim p, \sim q\}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, is :
Among the statements : \((S1)\) \((( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )\)\((S2)\)\((( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))\)
Equivalent statement to (p\(\to\)q) \(\vee\) (r\(\to\)q) will be
The number of seven-digit positive integers formed using the digits 1, 2, 3, and 4 only, and whose sum of the digits is 12, is
The fractional part of the number \(\tfrac{4^{2022}}{15}\) is equal to:
Negation of the Boolean statement (p ∨ q) ⇒ ((~ r) ∨ p) is equivalent to
Let\( Δ,▽∈{∧,∨} \)be such that \(p▽q⇒((pΔq)▽r) \)is a tautology. Then \((p▽q)Δr \)is logically equivalent to: