CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 5 - MCQExams.com

The contrapositive of $$\sim p \rightarrow ( q \rightarrow \sim r)$$ is
  • $$(~q \wedge r) \rightarrow ~p$$
  • $$(q \rightarrow r) \rightarrow~p$$
  • $$(q \vee ~r) \rightarrow ~ p$$
  • None of these.
Let $$S$$ be non-empty subset of $$R$$ then consider the following statement
 "Every number $$\displaystyle x\: \epsilon \: S $$ is an even number."
Negation of the statement will be
  • There is no number $$\displaystyle x\: \epsilon \: S $$ which is even
  • There exists a number $$\displaystyle x\: \epsilon \: S $$ which is not even
  • There exists a number $$\displaystyle x\: \epsilon \: S $$ which is odd
  • ($$B$$) and ($$C$$) both
The compound statement, "If you want to top the school, then you do not study hard" is equivalent to
  • "If you want to top the school, then you need to study hard".
  • "If you will not top in the school, then you study hard".
  • "If you study hard, then you will not top the school".
  • "If you do not study hard, then you will top in the school".
Which of the following is equivalent to $$p\Longleftrightarrow q$$?
  • $$p\implies q$$
  • $$q\implies p$$
  • $$(p\implies q)\wedge(q\implies p)$$
  • None of these
The property $$p\wedge(q\vee r)\equiv(p\wedge q)\vee(p\wedge r)$$ is called
  • associative law
  • commutative law
  • distributive law
  • idempotent law
Write the negation of the statement "If the switch is on, then the fan rotates".
  • "If the switch is not on, then the fan does not rotate".
  • "If the fan does not rotate, then the switch is not on".
  • "The switch is not on or the fan rotates".
  • "The switch is on and the fan does not rotate".
The negation of the statement, "I go to school everyday", is
  • I never go to school.
  • Some days, I do not go to school.
  • Not all the days I do not go to school.
  • All days I go to school.
In the above network, current flows from N to T when
399757.png
  • p closed, q closed, r opened and s opened.
  • p dosed, q opened, s closed and r opened.
  • q closed, p opened, r opened and s closed.
  • p opened, q opened, r closed and s closed.
Find the converse of the statement, "If ABCD is square, then it is a rectangle".
  • If ABCD is a square, then it is .not a rectangle.
  • If ABCD is not a square, then i is a rectangle.
  • if ABCD is a rectangle, then it is square.
  • If ABCD is not a square, then it is not a rectangle.
The counter example of the statement,  "All odd numbers are primes", is
  • 7
  • 5
  • 9
  • All the above
If "All odd numbers are primes and the sum of three angles in a triangle is $$190^\circ$$", then "All odd numbers are primes or the sum of the angles in a triangle is $$190^\circ$$" is a
  • tautology
  • contradiction
  • contingency
  • not a statement
In the above network, current flows from M to N, when
399756.png
  • q closed, r opened and p closed.
  • q opened, p opened and r closed.
  • q opened, p closed and r closed.
  • q closed, p closed and r opened.
Which of the following connectives can be used for describing a switching network?
  • $$\vee$$
  • $$\wedge$$
  • Both (1) and (2)
  • None of these
"No square of a real number is less than zero"  is equivalent to
  • for every real number a, $$a^2$$ is non negative.
  • $$\forall a\in R$$, $$a^2\ge0$$.
  • either (1) or (2).
  • None of these
Find the truth value of the statement, "The sum of any two odd numbers is an odd number".
  • True
  • False
  • Neither True nor False
  • Cannot be determined
The truth value of the statement, "We celebrate our Independence day on 15 August", is
  • T
  • F
  • neither T nor F
  • Cannot be determined
What is the truth value of the statement $$2\times3=6$$ or $$5+8=10$$?
  • True
  • False
  • Neither True nor False
  • Cannot be determined
The converse of converse of the statement $$p\implies\sim q$$ is
  • $$\sim q\implies p$$
  • $$\sim p\implies q$$
  • $$p\implies\sim q$$
  • $$\sim q\implies\sim p$$
Which of the following connectives satisfy commutative law?
  • $$\wedge$$
  • $$\vee$$
  • $$\Leftrightarrow$$
  • All the above
In which of the following cases, $$p\Leftrightarrow q$$ is true?
  • p is true, q is true.
  • p is false, q is true.
  • p is true, q is false.
  • None of these.
Write the compound statement, "If p, then q and if q, then p" in symbolic form.
  • $$(p\wedge q)\wedge(q\wedge p)$$
  • $$(p\implies q)\vee(q\implies p)$$
  • $$(q\implies p)\wedge(p\implies q)$$
  • $$(p\wedge q)\vee(q\wedge p)$$
When does the truth value of the statement $$(p\vee r)\Leftrightarrow (q\vee r)$$ become true?
  • p is true, q is true.
  • p is false, q is false.
  • p is true, r is true.
  • Both (1) and (3)
Find the negation of the statement, "Some odd numbers are not prime".
  • Some odd numbers are primes.
  • There is an odd number which is not a prime.
  • All odd numbers are primes.
  • Not all odd numbers are primes.
when does the current flow from A to B?

415009.png
  • p is open, q is open, r is closed.
  • p is closed, q is open, r is closed.
  • p is closed, q is closed, r is open.
  • p is open, q is closed, r is closed.
He is smart; He is intelligent.
Write the conjunction.
  • He is smart and he is intelligent.
  • He is smart maybe he is intelligent.
  •  He is intelligent because He is smart
  • He is not smart and he is not intelligent.
"If natural numbers are whole numbers, then rational numbers are integers" or "If rational numbers are integers, then natural numbers are whole numbers" is
  • a tautology
  • a contradiction
  • a contingency
  • not a statement
Find the inverse of the statement, "If $$\triangle{ABC}$$ is equilateral, then it is isosceles".
  • If $$\triangle{ABC}$$ is isosceles, then it is equilateral.
  • If $$\triangle{ABC}$$ is not equilateral, then it is isosceles.
  • If $$\triangle{ABC}$$ is not equilateral, then it is not isosceles.
  • If $$\triangle{ABC}$$ is not isosceles, then it is not equilateral.
In the above network, current flows from T to M, when
399793.png
  • p closed, q closed and r opened.
  • p closed, q opened and r closed.
  • p opened; q closed and r closed.
  • All the above
The compound statement, "If you won the race; then you did not run faster than others" is equivalent to
  • "If you won the race, then you ran faster than others".
  • "If you ran faster than others, then you won the race".
  • "If you did not win the race, then you did not run faster than others".
  • "If you ran faster than others, then you did not win the race".
Which of the following is negation of the statement "All birds can fly".
  • "Some birds cannot fly".
  • "All the birds cannot fly".
  • "There is at least one bird which can fly".
  • All the above
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