Mathematical reasoning practice · Mixed difficulty

If $(p \wedge \sim r) \Rightarrow(q \vee r)$ is false and $q$ and $r$ are both false, then $p$ is

The contrapositive of $(p \vee q) \Rightarrow r$ is

Consider the following statements.

Statement-I: The words "And" and "or" are connectives.

Statement-II: "There exists" and "For all" are called quantifiers.

If $\Delta \in\{\vee, \wedge\}$, then the negation of Boolean expression $(p \rightarrow p \vee q) \Delta(p \wedge q \rightarrow q)$ is

Consider the following three statements

$p:$ Person ‘A’ passed in Mathematics exam

$q:$ Person ‘A’ passed in Physics exam

$r:$ Person ‘A’ passed in Chemistry exam

The statement $\sim \left( {\left( { \sim \left( {p \Rightarrow q} \right)} \right) \Rightarrow r} \right)$ is equivalent to

Which of the following is not a statement?

Which of the following is equivalent to the Boolean expression $p \wedge \sim q?$

The Statement that is TRUE among the following is

The statement $p \rightarrow(q \rightarrow p)$ is equivalent is:

If I become a teacher, then I will open a school", is

The logically equivalent proposition of $p \Leftrightarrow q$ is

If $p:4$ an even prime number $q:6$ is a divisor of 12 and $r:$ the HCF of 4 and 6 is 2, then which one of the following is true?

Which of the following is false?

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

The contrapositive of the statement, "I $\mathrm{x}$ is a prime number and $\mathrm{x}$ divides $\mathrm{ab}$ then $\mathrm{x}$ divides $\mathrm{a}$ or $\mathrm{x}$ ivides b", can be symbolically represented using logical connectives, on apporpriately-defined statements $p, q, r, s$, as

Let $A$, $B$, $C$ and $D$ be four non-empty sets. The contrapositive statement of
"If $A\, \subseteq \,B$ and $B\, \subseteq \,D$, then $A\, \subseteq \,C$ " is

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

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

The negation of $x \in \mathrm{A} \cap \mathrm{B} \Rightarrow(x \in \mathrm{A}$ and $x \in \mathrm{B})$ is ......

Let $R$ be the set of real numbers and $x \in R$. Then, $x+3=8$ is

The proposition $p \to \, \sim \,(p \wedge \sim q)$ is equivalent to

Let

$p$ : Ramesh listens to music.

$q:$ Ramesh is out of his village.

$r$ : It is Sunday.

$s$ : It is Saturday.

Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as

If $(p \to (p \wedge \sim q)$ is false, then the truth values of p and q are respectively

The following statement $(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow[(\sim \mathrm{p} \rightarrow \mathrm{q}) \rightarrow \mathrm{q}]$ is:

Negation of statement : if we control population growth we prosper, is

The contrapositive of the statement “ If I reach the station in time, then I will catch the train” is

A compound sentence formed by two simple statements $p$ and $q$ using connective 'or' is called

The Boolean expression $(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$ is equivalent to

The contrapositive and converse of the statement ' 1 go to beach whenever it is a sunny day' is

Contrapositive of $p \rightarrow(q \rightarrow r)$ is logically equivalent to