Mathematical Reasoning

The symbolic form of the following circuit is (where \(p, q\) represents switches \(S_1\) and \(s_2\) closed respectively)

If \(p \rightarrow(\sim p \vee q)\) is false, then the truth values of \(p\) and \(q\) are respectively

The negation of the statement ' He is poor but happy' is

If \(p, q\) are true statement and \(r\) is false statement, then which of the following statements is a true statement.

Which of the following statement pattern is a tautology?

5. "If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, the inverse of the given statement is

Let $a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$ and $b:(p \vee s) \leftrightarrow(q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false, then the truth values of $a$ and $b$ are respectively......

The statement pattern $(p \wedge q) \wedge[\sim r \vee(p \wedge q)] \vee(\sim p \wedge q)$ is equivalent to ...........

Which of the following is not equivalent to $p \rightarrow q$.

The equivalent form of the statement $\sim(p \rightarrow \sim q)$ is $\ldots$

Which of the following statements is contingency?

The negation of " $\forall, n \in N, n+7>6$ " is .............

If $p$ and $q$ are true and $r$ and $s$ are false statements, then which of the following is true?