CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 2 - MCQExams.com

State the following statement is True or False
The truth value of "$$4$$ is even and $$8$$ is odd" is True
  • True
  • False
Which is logically equivalent to "If today is Sunday Matt cannot play hockey"?
  • Today is Sunday and Matt can play hockey
  • If Matt plays hockey then today is not Sunday
  • Today is Sunday and Matt cannot play hockey
  • Today is not Sunday if and only if Matt plays hockey
Which statement is logically equivalent to "If Yoda cannot use a lightsaber then he cannot help Luke win the battle" 
  • Yoda cannot use a lightsaber and he will help Luke win the battle
  • If Yoda can help Luke win the battle then he can use a lightsaber
  • Yoda can use a lightsaber if and only if he can help Luke win the battle
  • Yoda cannot use a lightsaber and will not help Luke win the battle
Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident.
  • If you lose the game then you dont know the rules or you are overconfident.
  • A sufficient condition that you win the game is that you know the rules or you are not overconfident.
  • If you dont know the rules or are overconfident you lose the game
  • If you know the rules and are overconfident then you win the game.
Which of the following statements is the inverse of "Our pond floods whenever there is a thunderstorm."?
  • If there is a thunderstorm, then our pond floods.
  • If we do not get a thunderstorm, then our pond does not flood.
  • If our pond does not flood, then we did not get a thunderstorm.
  • None of these
$$\sim \left[ \left( p\wedge q \right) \rightarrow \left( \sim p\vee q \right) \right]$$ is
  • Tautology
  • Contradiction
  • Neither (A) nor (B)
  • Either (A) or (B)
Which of the following statements is the converse of "You cannot skateboard if you do not have a sense of balance."?
  • If you cannot skateboard, then you do not have a sense of balance.
  • If you do not have a sense of balance, then you cannot skateboard.
  • If you skateboard, then you have a sense of balance.
  • None of these
Which of the following statements is the inverse of "If it rains, then I do not go fishing."?
  • If I go fishing, then it does not rain.
  • If I do not go fishing, then it rains.
  • If it does not rain, then I go fishing.
  • None of these
The negative of the statement "he is rich and happy" is given by
  • He is not rich and not happy
  • He is not rich or not happy
  • He is rich and happy
  • He is not rich and happy
The inverse of the statement "If it is raining then the grass is wet"
  • "If it is not raining then the grass is not wet".
  • "If it is raining then the grass is not wet".
  • "If it is not raining then the grass is wet".
  • None of these
Which of the following statements is logically equivalent to "The solution is easy if you read the question carefully."?
  • If you do not read the question carefully, the solution is hard.
  • If the solution is easy, then you read the question carefully.
  • If the solution is hard, then you did not read the question carefully.
  • None of these
If p : A man is happy
   q : A man is rich
Then, the statement, "If a man is not happy, then he is not rich" is written as
  • $$\sim p\rightarrow \sim q$$
  • $$\sim q\rightarrow p$$
  • $$\sim q\rightarrow \sim p$$
  • $$q\rightarrow \sim p$$
The inverse of the statement " If a person is mean, then they are a fighter " is-
  • If a person is not mean, then they are not a fighter.
  • If a person is not mean, then they are a fighter.
  • If a person is mean, then they are not a fighter.
  • None of the above
Negation of the statement "Every natural number is an integer".
  • All natural numbers are whole numbers.
  • Every natural number is not an integer.
  • Every natural number is not a real number.
  • none of the above
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  • Assertion is correct but Reason is incorrect
  • Assertion is incorrect but Reason is correct
The inverse of the statement "If a number is divisible by 4 then it is also divisible by 2" is-
  • If a number is divisible by 4, then it is always divisible by 2.
  • If a number is not divisible by 4, then it is divisible by 2.
  • If a number is not divisible by 4, then it is not divisible by 2.
  • None of the above
Inverse of the statement "If the triangle with side lengths $$a, b, c$$ is a right triangle, then $$a^2 + b^2 = c^2$$.
  • If $$a^2+b^2\neq c^2$$ then the triangle with side lengths $$a, b, c$$ is not a right triangle.
  • If $$a^2+b^2 = c^2$$ then the triangle with side lengths $$a, b, c$$ is a right triangle.
  • If the triangle with side lengths $$a,b,c$$ is a not right triangle, then $$a^2 + b^2 \neq c^2$$.
  • None of the above.
Which of the following is a statement?
  • Rani is a beautiful girl.
  • Shut the door.
  • Yesterday was Friday..
  • If its raining then there must be cloud in the sky.
Write the inverse of the statement- 
If you do not drink your milk, you will not be strong.
  • If you are strong, then you drink your milk,
  • If you do not drink your milk, then you are strong.
  • If you drink your milk, then you are strong.
  • None of the above
Inverse of a statement can be explained as
  • Negating both the hypothesis and conclusion of a conditional statement.
  • Antecedent is the negation of the original antecedent and whose consequent is the negation of the original consequent.
  • both are correct
  • none is correct
State whether true or false.
The sum of the interior angles of a quadrilateral is $$350^o$$.
  • True
  • False
State whether the following statements are true or false. Give reasons for your answers.
For any real number $$x, x^2 \geq 0$$.
  • True
  • False
State true or false.
A rhombus is a parallelogram.
  • True
  • False
State whether the following statement is true or false.
The sum of two even numbers is even.
  • True
  • False
If a compound statement is made up of three simple statements, then the number of rows in the truth table is
  • $$8$$
  • $$6$$
  • $$4$$
  • $$2$$
If truth values of $$p$$ be $$F$$ and $$q$$ be $$T$$. Then, truth value of $$\sim (\sim p\vee q)$$ is
  • $$T$$
  • $$F$$
  • Either $$T$$ or $$F$$
  • Neither $$T$$ not $$F$$
The converse of the contrapositive of the conditional $$ p \rightarrow \sim q $$ is : 
  • $$ p \rightarrow q $$
  • $$ \sim p \rightarrow \sim q $$
  • $$ \sim q \rightarrow p $$
  • $$ \sim p \rightarrow q $$
Let $$p, q$$ and $$r$$ be any three logical statements. Which one of the following is true?
  • $$\sim [p \wedge (\sim q)] \equiv (\sim p )\wedge  q$$
  • $$\sim (p \vee q) \wedge  (\sim r) \equiv (\sim p) \vee (\sim q) \vee (\sim r)$$
  • $$\sim [p \vee (\sim q)] \equiv (\sim p) \wedge q$$
  • $$\sim [p \wedge (\sim q)] \equiv (\sim p) \wedge \sim q$$
  • $$\sim [p \wedge (\sim q)] \equiv p \wedge q$$
"If we control population growth, then we prosper". Negative of this proposition is:
  • If we do not control population growth, we prosper
  • If we control population, we do not prosper
  • we control population and we do not prosper
  • If we don't control population, we do not prosper
Which one of the following statement is a tautology?
  • $$p\rightarrow (p\rightarrow q)$$
  • $$(p \vee p)\rightarrow q$$
  • $$p \vee (p\rightarrow q)$$
  • $$p \vee (q\rightarrow p)$$
0:0:1


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