Boolean expression left( {left( {p wedge q} right) vee left( {p vee ∼ q} right)} right

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Mathematical Reasoning

hard

The Boolean expression $\left( {\left( {p \wedge q} \right) \vee \left( {p \vee \sim q} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$ is equivalent to

$p \wedge q$

$p \wedge \left( { \sim q} \right)$

$\left( { \sim p} \right) \wedge \left( { \sim q} \right)$

$p \vee \left( { \sim q} \right)$

(JEE MAIN-2019)

Solution

$\left( {\left\{ {\left( {p \wedge q} \right) \vee p} \right\} \vee \left\{ {\left( {p \wedge q} \right) \vee \sim q} \right\}} \right) \wedge \sim \left( {p \vee q} \right) \equiv $

$\left\{ {p \vee \left( {p \vee \sim q} \right) \wedge \left( {q \vee \sim q} \right)} \right\} \wedge \sim \left( {p \vee q} \right)$

$\left( {p \vee \left\{ {p \vee \sim q} \right\}} \right) \wedge \left( {p \vee q} \right) \equiv \left( {p \vee \sim q} \right) \wedge \sim \left( {p \vee q} \right) \equiv \sim p \wedge \sim q$

Standard 11

Mathematics

The statement $(p \Rightarrow q) \vee(p \Rightarrow r)$ is NOT equivalent to.

medium

(JEE MAIN-2022)

Which of the following is a contradiction

medium

The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $( p \Delta q ) \Rightarrow(( p \Delta \sim q ) \vee((\sim p ) \Delta q ))$ is a tautology, is

medium

(JEE MAIN-2022)

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

medium

(JEE MAIN-2022)

Consider the following three statements :
$P : 5$ is a prime number.
$Q : 7$ is a factor of $192$.
$R : L.C.M.$ of $5$ and $7$ is $35$.
Then the truth value of which one of the following statements is true?

hard

(JEE MAIN-2019)

The Boolean expression $\left( {\left( {p \wedge q} \right) \vee \left( {p \vee \sim q} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$ is equivalent to

Solution

Similar Questions

The statement $(p \Rightarrow q) \vee(p \Rightarrow r)$ is NOT equivalent to.

Which of the following is a contradiction

The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $( p \Delta q ) \Rightarrow(( p \Delta \sim q ) \vee((\sim p ) \Delta q ))$ is a tautology, is

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

Consider the following three statements : $P : 5$ is a prime number. $Q : 7$ is a factor of $192$. $R : L.C.M.$ of $5$ and $7$ is $35$. Then the truth value of which one of the following statements is true?

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Consider the following three statements :
$P : 5$ is a prime number.
$Q : 7$ is a factor of $192$.
$R : L.C.M.$ of $5$ and $7$ is $35$.
Then the truth value of which one of the following statements is true?