Mathematical Reasoning Questions - JEE

Maximum number of compound propositions from $p\wedge q\wedge r$, $p\wedge\sim q\wedge r$, $p\wedge q\wedge\sim r$, $\sim p\wedge q\wedge s$, $\sim p\wedge q\wedge s$, $q\wedge r\wedge s$, $q\wedge\sim r\wedge s$, $\sim q\wedge r\wedge\sim s$ that can be simultaneously false is

The compound statement $(\sim p \vee q) \wedge (\sim p \wedge \sim q)$ is

Consider statements $P$: Sachin is a topper; $Q$: Sachin is sincere; $R$: Sachin is not demotivated. The negation of the statement 'If Sachin is sincere and he is not demotivated, then he is a topper' is

The compound statement $(\sim(P \wedge Q)) \vee ((\sim P) \wedge Q) \Rightarrow ((\sim P) \wedge (\sim Q))$ 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 $\{(p \vee q) \wedge ((\sim p) \vee r)\} \to ((\sim q) \vee r)$ false?

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:

The negation of the expression $q \vee ((\sim q) \wedge p)$ is equivalent to

Consider statements $P$: Sachin is a topper; $Q$: Sachin is sincere; $R$: Sachin is not demotivated. The negation of the statement 'If Sachin is sincere and he is not demotivated, then he is a topper' is

The proposition $p \rightarrow \neg(p \wedge \neg q)$ is equivalent to

The negation of the boolean expression $(p \rightarrow (q \rightarrow p)) \rightarrow \neg s \vee (\neg r \wedge s)$ is equivalent to

The compound statement $(\sim p \vee q) \wedge (\sim p \wedge \sim q)$ is

$(\neg p \Rightarrow p) \wedge (p \Rightarrow \neg q)$

Can both be $\Rightarrow$?

Consider the following statements: P: I have fever; Q: I will not take medicine; R: I will take rest. The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:

If $p$ and $q$ are two logical statements, then $p \iff q$ (as $p \Leftrightarrow q$) is equivalent to

The negation of $p ∧ (q → r)$ is

The statement $(p \rightarrow (q \rightarrow p)) \rightarrow (p \rightarrow (p \vee q))$ is

The logically equivalent proposition of $p ↔ q$ is

The contrapositive of the statement "If two triangles are identical, then they are similar" is

If $p → (¬ p ∨ q)$ is false, then the truth values of $p$ and $q$ are respectively

If $p → (q ∨ r)$ is False, then the truth values of $p, q, r$ are respectively (where $T$ is True and $F$ is False)

Which of the following is incorrect?

Statement $S_1$ and $S_2$ evaluation for true/false classification

The compound statement $(\sim p \vee q) \wedge (\sim p \wedge \sim q)$ is

Consider statements $P$: Sachin is a topper; $Q$: Sachin is sincere; $R$: Sachin is not demotivated. The negation of the statement 'If Sachin is sincere and he is not demotivated, then he is a topper' is

If $p$: A man is happy and $q$: A man is rich are two statements, then the statement, "If a man is not happy, then he is not rich" can be written using logical operators as

Let $p$ and $q$ be two statements. Then $\sim(p \wedge (p \Rightarrow \sim q))$ is equivalent to

(S1) $(p \Rightarrow q) \vee (p \wedge (\sim q))$ is a tautology. (S2) $((\sim p) \Rightarrow (\sim q)) \wedge ((\sim p) \vee q)$ is a Contradiction. Then

The statement $B \Rightarrow ((\sim A) \vee B)$ is equivalent to

Let $\Delta, \nabla \in \{\wedge, \vee\}$ be such that $(p \to q)\Delta(p\nabla q)$ is a tautology. Then

Which of the following statements is a tautology?

Among the statements: (S1) $((p \vee q) \Rightarrow r) \Leftrightarrow (p \Rightarrow r)$ and (S2) $((p \vee q) \Rightarrow r) \Leftrightarrow ((p \Rightarrow r) \vee (q \Rightarrow r))$

$p$ is true and $(y \vee r)$ is false

The statement $(p \wedge (\sim q)) \Rightarrow (p \Rightarrow (\sim q))$ is

Maximum number of compound propositions from $p\wedge q\wedge r$, $p\wedge\sim q\wedge r$, $p\wedge q\wedge\sim r$, $\sim p\wedge q\wedge s$, $\sim p\wedge q\wedge s$, $q\wedge r\wedge s$, $q\wedge\sim r\wedge s$, $\sim q\wedge r\wedge\sim s$ that can be simultaneously false is

Mathematical Reasoning Questions (36)