CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 3 - MCQExams.com

The converse of $$p\Rightarrow q$$ is
  • $$p\Rightarrow q$$
  • $$q\Rightarrow p$$
  • $$-p\Rightarrow -q$$
  • $$-q \Rightarrow -p$$
$$P\rightarrow (q\rightarrow r)$$ is logically equivalent to
  • $$(q\vee q)\rightarrow \sim r$$
  • $$(p\wedge q)\rightarrow \sim r$$
  • $$(p\vee q)\rightarrow r$$
  • $$(p\wedge q)\rightarrow r$$
The negation of the statement $$(p\rightarrow q)\wedge r$$ is
  • $$p\wedge \sim q\vee \sim r$$
  • $$(\sim p\wedge q)\wedge (\sim r)$$
  • $$(p\wedge \sim q)\wedge (r)$$
  • $$(p\wedge \sim q)\wedge (\sim r)$$
$$p\vee q$$ is true, when 
  • either $$p$$ of $$q$$ are true
  • $$p$$ is true and $$q$$ is false
  • $$p$$ is false and $$q$$ is true
  • All of these
Contrapositive of the statement  ''if two number are not equal then their square are not equal is ; 
  • If the squares of two number are equal , then the number are not equal
  • If the squares of two number are equal  , then the number are equal
  • If the square of two number are not equal then number are equal
  • If the square of two number are not, equal , then the number are not equal
State whether the following statement is True or False.
The sum of three odd numbers is even.
  • True
  • False
State whether the following statement is True or False.
The product of two even numbers is always even.
  • True
  • False
State whether the following statement is True or False.
All even numbers are composite numbers.
  • True
  • False
State whether the following statement is True or False.
If an even number is divided by $$2$$, the quotient is always odd.
  • True
  • False
State whether the following statement is True or False.
$$2$$ is the only even prime number.
  • True
  • False
State whether the statement
$$p:$$ If $$x$$ is a real number such hat $$x^{3}+x=0$$ , then $$x$$ is $$0$$ is true/false
  • True
  • False

State whether the statements given are True or False

Two rational with different numerators can never be equal
  • True
  • False
Select and write the correct answer from the given alternative of the following question:
If $$ p \wedge q $$ is false and $$ p \wedge q $$ is true, then __________ is not true.
  • $$ p \vee q $$
  • $$ p \leftrightarrow q $$
  • $$ \sim p\, \vee \, \sim q $$
  • $$ q \vee \, \sim p $$
Select and write the correct answer from the given alternative of the following question:
Inverse of statement pattern $$ (p \vee q) \rightarrow (p \wedge q) $$ is ________.
  • $$ (p \wedge q) \rightarrow (p \vee q) $$
  • $$ \sim (p \vee q) \rightarrow (p \wedge q) $$
  • $$ (\sim p \wedge \, \sim q) \rightarrow (\sim p \vee \, \sim q) $$
  • $$ (\sim p \vee \, \sim q) \rightarrow (\sim p \, \wedge \, \sim q) $$
Select and write the correct answer from the given alternative of the following question:
If $$ A =  \left \{1 , 2 , 3 , 4 , 5  \right  \} $$ then which of the following is not true ?
  • $$ \exists \, x \, \in \, A $$ such that $$ x + 3 = 8 $$
  • $$ \exists \, x \, \in \, A $$ such that $$ x + 2 < 9 $$
  • $$ \forall \, x \, \in \, A , x + 6 \geq 9 $$
  • $$ \exists \, x \, \in \, A $$ such that $$ x + 6 < 10 $$
Select and write the correct answer from the given alternative of the following question:
The negation of inverse of $$ \sim p \rightarrow q $$ is ___________.
  • $$ q \wedge p $$
  • $$ \sim p \wedge\, \sim q $$
  • $$ p \wedge q $$
  • $$ \sim q \rightarrow \, \sim p $$
Select and write the correct answer from the given alternative of the following question:
If $$ p \wedge q $$ is F , $$ p \rightarrow q $$ is F then the truth values of $$p$$ and $$q$$ are ___________.
  • T , T
  • T , F
  • F , T
  • F , F
Select and write the correct answer from the given alternative of the following question:
The negation of $$ p \wedge (q \rightarrow r) $$ is __________.
  • $$ \sim p \wedge (\sim q \rightarrow \, \sim r) $$
  • $$ p \vee (\sim q \vee r) $$
  • $$ \sim p \wedge (\sim q \rightarrow \, \sim r) $$
  • $$ \sim p \vee (\sim q \wedge \sim r) $$
 $$p\wedge (\sim p) \Rightarrow p$$ is 
  • a tautology
  • a contradiction
  • neither tautology nor contradiction
  • none of these
$$p$$: He is hard working.
$$q$$: He is intelligent.
Then $$ \sim q\Rightarrow\sim p$$, represents
  • If he is hard working, then he is not intelligent.
  • If he is not hard working, then he is intelligent.
  • If he is not intelligent, then he is not had working.
  • If he is not intelligent, then he is hard working.
The contrapositive of "if in a triangle $$ABC, AB=AC$$, then $$\angle B=\angle C$$", is
  • If in a triangle $$ABC, \angle B=\angle C$$, then $$AB=AC$$.
  • If in a triangle $$ABC, AB\neq AC$$, then $$\angle B\neq\angle C$$.
  • If in a triangle $$ABC, \angle B\neq\angle C$$, then $$AB\neq AC$$.
  • If in a triangle $$ABC, \angle B\neq\angle C$$, then $$AB=AC$$.
$$p:$$ He is hard working.
$$q:$$ He will win.
The symbolic form of "If he will not win then he is not hard working", is
  • $$ p\Rightarrow q$$
  • $$ (\sim p)\Rightarrow (\sim q)$$
  • $$ (\sim q)\Rightarrow (\sim p)$$
  • $$ (\sim q)\Rightarrow p$$
The converse of: "If two triangles are congruent then they are similar" is
  • If two triangles are similar then they are congruent.
  • If two triangles are not congruent then they are not similar.
  • If two triangles are not similar then they are not congruent.
  • None
The contrapositive of $$  p\Rightarrow q$$, is
  • $$ p\Rightarrow q$$
  • $$ q\Rightarrow p$$
  • $$ \sim p\Rightarrow \sim q$$
  • $$ \sim q\Rightarrow \sim p$$
The inverse of "If $$x$$ has courage, then $$x$$ will win", is
  • If $$x$$ will win, then $$x$$ has courage.
  • If $$x$$ has no courage, then $$x$$ will not win.
  • If $$x$$ will not win, then $$x$$ has no courage.
  • If $$x$$ will not win, then $$x$$ has courage.
$$p:$$ He is hard working.
$$q:$$ He will win.
The symbolic form of "He is hard working then he will win", is
  • $$p\vee q$$
  • $$p\wedge q$$
  • $$p \Rightarrow q$$
  • $$q \Rightarrow p$$
The converse of "If in a triangle $$ABC, AB=AC$$, then $$\angle B=\angle C$$", is
  • lf in a triangle $$ABC, \angle B=\angle C$$, then $$AB=AC$$.
  • lf in a triangle$$ABC, AB\neq AC$$, then $$\angle B\neq\angle C$$.
  • lf in a triangle $$ABC, \angle B\neq\angle C$$, then $$AB\neq AC$$.
  • lf in a triangle $$ABC, \angle B\neq\angle C$$, then $$AB=AC$$ .
The converse of $$ p\Rightarrow q$$, is
  • $$ p\Rightarrow q$$
  • $$ q\Rightarrow p$$
  • $$ \sim p\Rightarrow \sim q$$
  • $$ \sim q\Rightarrow \sim p$$
The inverse proposition of $$(p \wedge \sim q)\Rightarrow r$$, is
  • $$\sim r \Rightarrow \sim p\vee q$$
  • $$\sim p\vee q \Rightarrow \sim r$$
  • $$r \Rightarrow p\wedge \sim q $$
  • none of these.
Which of the following is the inverse of the proposition "If a number is prime, then it is odd"?
  • If a number is not prime, then it is odd.
  • If a number is not a prime, then it is not odd.
  • If a number is not odd, then it is not a prime.
  • If a number is not odd, then it is a prime.
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