Releted MCQ Question on
Algebra >> Mathematical Reasoning
Releted Question 1
Let $$p$$ be the statement “$$x$$ is an irrational number”, $$q$$ be the statement “$$y$$ is a transcendental number”, and $$r$$ be the statement “$$x$$ is a rational number if $$f y$$ is a transcendental number”.
Statement - 1 : $$r$$ is equivalent to either $$q$$ or $$p$$
Statement - 2 : $$r$$ is equivalent to $$ \sim \left( {p \leftrightarrow \sim q} \right).$$
A.
Statement - 1 is false, Statement - 2 is true
B.
Statement - 1 is true, Statement - 2 is true ; Statement - 2 is
a correct explanation for Statement - 1
C.
Statement - 1 is true, Statement - 2 is true ; Statement - 2
is not a correct explanation for Statement - 1
D.
none of these
Releted Question 2
The statement $$p \to \left( {q \to p} \right)$$ is equivalent to
A.
$$p \to \left( {p \to q} \right)$$
B.
$$p \to \left( {p \vee q} \right)$$
C.
$$p \to \left( {p \wedge q} \right)$$
D.
$$p \to \left( {p \leftrightarrow q} \right)$$
Releted Question 3
Statement - 1 : $$ \sim \left( {p \leftrightarrow \sim q} \right)$$ is equivalent to $${p \leftrightarrow q}.$$
Statement - 2 : $$ \sim \left( {p \leftrightarrow \sim q} \right)$$ is a tautology
A.
Statement - 1 is true, Statement - 2 is true;
Statement - 2 is not a correct explanation for Statement - 1.
B.
Statement - 1 is true, Statement - 2 is false.
C.
Statement - 1 is false, Statement - 2 is true.
D.
Statement - 1 is true, Statement - 2 is true,
Statement - 2 is a correct explanation for statement - 1
Releted Question 4
Consider the following statements
$$P$$ : Suman is brilliant
$$Q$$ : Suman is rich
$$R$$ : Suman is honest
The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as
A.
$$ \sim \left( {Q \leftrightarrow \left( {P \wedge \sim R} \right)} \right)$$
B.
$$ \sim Q \leftrightarrow \sim P \wedge R$$
C.
$$ \sim \left( {P \wedge \sim R} \right) \leftrightarrow Q$$
D.
$$ \sim P \wedge \left( {Q \leftrightarrow \sim R} \right)$$