MCA Entrance Previous Year Question Bank

Negation of the Boolean statement $(p\vee q)\Rightarrow ((\sim r)\vee p)$ is equivalent to:

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

Which of the following statements is a tautology?

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

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:

(S1) $(p⟹q)\vee (p\wedge (\sim q))$ is a tautology

(S2) $((\sim p)⟹(\sim q))\wedge ((\sim p)\vee q)$ is a contradiction.

Then

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:

Among the statements:

(S1) $((p\vee q)\Rightarrow r)\iff (p\Rightarrow r)$

(S2) $((p\vee q)\Rightarrow r)\iff ((p\Rightarrow r)\vee (q\Rightarrow r))$

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

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