CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 7 - MCQExams.com

The inverse of statement "If a dog is barking, then it will not bite" is
  • If a dog is not barking, then it will bite.
  • If a dog is biting, then it will not bark.
  • If a dog is not biting, then it will not bark.
  • None of the above
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 the above
Which of the following statements is the inverse of 
"If you do not understand geometry, then you do not know how to reason deductively." ?
  • If you reason deductively, then you understand geometry.
  • If you understand geometry, then you reason deductively.
  • If the do not reason deductively, then you understand geometry.
  • None of the above
If $$x+4=8$$, then $$x=4$$, Inverse of the statement is-
  • If $$x+4=8$$, then $$x\neq4$$
  • If $$x+4\neq8$$, then $$x\neq4$$
  • If $$x+4\neq8$$, then $$x=4$$
  • none of the above
Which statement represents the inverse of the statement "If it is snowing, then Skeeter wears a sweater."?
  • If Skeeter wears a sweater, then it is snowing.
  • If Skeeter does not wear a sweater, then it is not snowing.
  • If it is not snowing, then Skeeter does not wear a sweater.
  • If it is not snowing, then Skeeter wears a sweater.
Write negation of:
All  natural numbers are integers  and all integers are not natural numbers.
  • All natural numbers are not integers and all integers are not natural numbers.
  • All natural numbers are integers and all integers are natural numbers.
  • Some natural numbers are integers and all integers are not natural numbers.
  • All natural numbers are not integers and some integers are natural numbers.
If $$p, q, r$$ are simple proportions with truth values $$T, F, T$$, then the truth value of $$(\sim p\vee q)\wedge \sim r \Rightarrow p$$ is
  • True
  • False
  • True, if $$r$$ is false
  • True, if $$q$$ is true
$$\sim \left[ p\wedge (\sim q) \right] =$$
  • $$\sim p \ \wedge \sim q$$
  • $$\sim p \ \vee \sim q$$
  • $$\sim p \ \wedge \ q$$
  • $$\sim p\vee q$$
The inverse of the propositions $$(p \wedge \sim q) \rightarrow r$$ is____.
  • $$(\sim r) \rightarrow (\sim p) \vee q$$
  • $$(\sim p)\vee q \rightarrow (\sim p) $$
  • $$r \rightarrow p \vee (\sim q)$$
  • $$(\sim p) \wedge (\sim q) \rightarrow r$$
$$p \leftrightarrow q$$ is equivalent to
  • $$p \rightarrow q$$
  • $$q \rightarrow p$$
  • $$(p \rightarrow q) \vee (q \rightarrow p)$$
  • $$(p \rightarrow q) \wedge (q \rightarrow p)$$
If $$p$$ is $$T$$ and $$q$$ is $$F$$, then which of the following have the truth value $$T$$?
$$(i)p\vee q$$
$$(ii)\sim p\vee q$$
$$(iii)p\vee (\sim q)$$
$$(iv)p\wedge (\sim q)$$
  • $$(i),(ii),(iii)$$
  • $$(i),(ii),(iv)$$
  • $$(i),(iii),(iv)$$
  • $$(ii),(iii),(iv)$$
If $$p:3$$ is a prime number and $$q:$$ one plus one is three, then the compound statement "It is not that $$3$$ is a prime number or it is not that one plus one is three" is
  • $$\sim p\vee q$$
  • $$\sim (p\vee q)$$
  • $$p\wedge \sim q$$
  • $$\sim p\vee \sim q$$
  • $$p\vee \sim q$$
If $$p$$'s truth value is $$T$$ and $$q$$'s truth value is $$F$$, then which of the following have the truth value $$T$$?
(i) $$p\vee q$$
(ii) $$\sim p\vee q$$
(iii) $$p\vee (\sim q)$$
(iv) $$p\wedge (\sim q)$$
  • (i), (ii), (iii)
  • (i), (iii), (iv)
  • (i), (ii), (iv)
  • (ii), (iii), (iv)
Which of the following is not a logical statement?
  • $$8$$ is less than $$6$$
  • Every set is a finite set
  • Kashmir is far from here
  • The sun is a star
The truth values of $$p, q$$ and $$r$$ for which $$(p \wedge q) \vee (\sim r)$$ has truth value F are respectively
  • F, T, F
  • F, F, F
  • T, T, T
  • T, F, F
  • F, F, T
$$\left( p\wedge \sim q \right) \wedge \left( \sim p\wedge q \right) $$ is a :
  • A tautology
  • A contradiction
  • Both a tautology and a contradiction
  • Neither a tautology nor a contradiction
If p, q, r have truth values T, F, T respectively, then which of the following is $$\text{True}$$?
  • $$(p\rightarrow q)\wedge r$$
  • $$(p\rightarrow q)\wedge \sim r$$
  • $$(p \wedge q)\wedge (p\vee r)$$
  • $$q\rightarrow (p\wedge r)$$
$$\sim [(\sim p) \wedge q]$$ is logically equivalent to
  • $$\sim (p \vee q)$$
  • $$\sim [p \wedge (\sim q)]$$
  • $$p \wedge (\sim q)$$
  • $$p \vee (\sim q)$$
  • $$(\sim p) \vee (\sim q)$$
The contrapositive statement of statement "If x is prime number, then x is odd" is
  • If X is not is prime number, then x is not odd
  • If X is not odd, then x is not a prime number
  • If X is a prime number, then x is not odd
  • If X is not a prime number, then x is odd
Let
$$p:57$$ is an odd prime number
$$q:4$$ is a divisor of $$12$$
$$r:15$$ is the LCM of $$3$$ and $$5$$
be three simple logical statements. Which one of the following is true?
  • $$p\vee (\sim q\wedge r)$$
  • $$\sim p\vee (q\wedge r)$$
  • $$(p\wedge q)\vee \sim r$$
  • $$(p\vee (q\wedge r)$$
  • $$(p\vee q)\wedge r$$
The converse of the contrapositive of the conditional $$p\rightarrow \sim q$$ is.
  • $$p\rightarrow q$$
  • $$\sim p \rightarrow \sim q$$
  • $$\sim q \rightarrow p$$
  • $$\sim p \rightarrow q$$
Given the true statement: If a quadrilateral is a square, then it is a rectangle. It follows that, of the converse and the inverse of this true statement.
  • Only the converse is true
  • Only the inverse is true
  • Both are true
  • Neither is true
  • The inverse is true, but the converse is sometimes true
If $$p\vee q$$ is true and $$p\wedge q$$ is false, then which of the following is not true?
  • $$p\vee q$$
  • $$p\leftrightarrow q$$
  • $$\sim p\vee \sim q$$
  • $$q\vee \sim q$$
Given are three positive integers $$a, b,$$ and $$c$$. Their greatest common divisor is $$D$$; their least common multiple is $$M$$. Then, which two of the following statements are true?
$$(1)$$ The product $$MD$$ cannot be less than $$abc$$
$$(2)$$ The product $$MD$$ cannot be greater than $$abc$$
$$(3)$$ $$MD$$ equals $$abc$$ if and only if $$a, b, c$$ are each prime
$$(4)$$ $$MD$$ equals $$abc$$ if and only if $$a, b, c$$ are relatively prime in pairs
(This means : no two have a common factor greater than $$1$$.)
  • $$1, 2$$
  • $$1, 3$$
  • $$1, 4$$
  • $$2, 3$$
  • $$2, 4$$
Given the following six statements:
(1) All women are good drivers
(2) Some women are good drivers
(3) No men are good drivers
(4) All men are bad drivers
(5) At least one man is a bad driver 
(6) All men are good drivers.
The statement that negates statement (6) is:
  • (1)
  • (2)
  • (3)
  • (4)
  • (5)
Which one of the following statements is not true for the equation
$$i{ x }^{ 2 }-x+2i=0$$.
where $$i\equiv \sqrt { -1 } $$?
  • The sum of the roots is $$2$$
  • The discriminant is $$9$$
  • The roots are imaginary
  • The roots can be found by using the quadratic formula
  • The roots can be found by factoring, using imaginary numbers
The moment of inertia of the plate about the $$x-$$axis is 
  • $$\dfrac{{M{L^2}}}{8}$$
  • $$\dfrac{{M{L^2}}}{32}$$
  • $$\dfrac{{M{L^2}}}{24}$$
  • $$\dfrac{{M{L^2}}}{6}$$
Negation of $$p \rightarrow ( p \vee \sim q )$$  is
  • $$\sim p \rightarrow ( \sim p \vee q )$$
  • $$p \wedge ( \sim p \wedge q )$$
  • $$\sim p \vee ( \sim p \vee \sim q )$$
  • $$\sim p \leftarrow ( \sim p \rightarrow q )$$
The negation of $$q\vee \sim (p\wedge r)$$ is?
  • $$\sim q\wedge \sim (p\vee r)$$
  • $$\sim q\wedge (p\wedge r)$$
  • $$\sim q\vee (p\wedge r)$$
  • $$\sim r\vee(p\wedge r)$$
Dual of $$( p \rightarrow q ) \rightarrow r$$ is _________________.
  • $$p\vee (\sim  q\wedge r)$$
  • $$p\vee q\wedge r$$
  • $$p\vee (\sim  q\wedge \sim r)$$
  • $$\sim p\vee (\sim q\wedge r)$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Maths Quiz Questions and Answers