CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 8 - MCQExams.com

P: he studies hard, q: he will get good marks. The symbolic form of " If he studies hard then he will get good marks "is_____
  • $$\sim q\Rightarrow p$$
  • $$p\Rightarrow q$$
  • $$\sim p\vee q$$
  • $$p\Leftrightarrow q$$
Consider the following two statements :
P:   If 7 is odd number, then is divisible by $$2$$.
Q:   If 7 is a prime number, Then is an odd number.
If $${ V }_{ 1 }$$ is the value of the contra-positive of $$p$$ and $${ V }_{ 2 }$$ Is the truth value of contra-positive of Q, then the orders pair $$({ V }_{ 1 },{ V }_{ 2 })$$ equals :
  • $$(T,T)$$
  • $$(T,F)$$
  • $$(F,T)$$
  • $$(F,F)$$
Negation of compound proposition : If the examination is difficult, then I shall pass if I study hard
  • The examination is difficult and I study hard and I shall pass
  • The examination is difficult and I study hard but I shall not pass
  • The examination is not difficult and I study hard and I shall pass
  • All of these
The cost of an article including the sales tax is $$Rs\ .616$$. The rate of sales tax is $$10\%$$,if the shopkeeper has made a profit of $$12\%$$ , then the cost price of the article is?
  • $$Rs\ .350$$
  • $$Rs\ .400$$
  • $$Rs\ .500$$
  • $$Rs\ .800$$
Consider the following statement
p:you want to success
q:you will find a away,
then the negation of $$\sim \left( p\ \nu\ q \right) $$
  • you want success or you will find a way
  • you want of success and you do not find a way
  • if you want of success then you cannot find a way
  • if you do not want to succeed then you will not find a way
If $$p, q, r$$ are three propositions, then the negation of $$p\rightarrow (q\wedge r)$$ is logically equivalent to
  • $$(p\vee\sim q)\wedge (p \vee\sim r)$$
  • $$(p\wedge \sim q)\vee (p\wedge\sim r)$$
  • $$(\sim p\vee q)\wedge (\sim p\vee r)$$
  • $$(\sim p\wedge q)\vee (\sim p\wedge r)$$
If statement $$(p\rightarrow q)\rightarrow (q\rightarrow r)$$ is false, then truth values of statements $$p,q,r$$ respectively, can be :
  • $$FTF$$
  • $$TTT$$
  • $$FFF$$
  • $$FTT$$
Negation of $$(\sim p\rightarrow q)$$ is ________________.
  • $$\sim { p }{ \wedge }\sim q$$
  • $$\sim \left( p\vee q \right) \vee \left( p\vee \left( \sim p \right) \right) $$
  • $$\sim \left( p\vee q \right) \wedge \left( p\vee \left( \sim p \right) \right) $$
  • $$\left( \sim p\vee q \right) \wedge \left( p\vee \sim q \right) $$
$$p \wedge ( q \vee \sim p ) =?$$
  • $$p \vee q$$
  • $$p \wedge q$$
  • $$p \rightarrow  q$$
  • none of these
Consider the statement "if it is raining, then sky is not filled with clouds which among the Q 7 following is true
  • contrapositive of the given statement "if sky is filled with clouds then it is not raining"
  • converse of the given statement is "If sky is filled with clouds then it is raining"
  • "If it is not raining then sky is filled with clouds" is the inverse of the given statement
  • Both 1 , 2 and 3 are true
The statement $$P \rightarrow ( q \vee r )$$ is not equivalent to
  • $$( p \rightarrow q ) \vee ( q - r )$$
  • $$p \wedge ( \sim q ) \rightarrow r$$
  • $$P \wedge ( \sim r ) \rightarrow q$$
  • $$p \wedge q \rightarrow ( p \wedge r ) \vee ( q \wedge r )$$
The false statement in the following is
  • $$p \wedge ( \sim p )$$ is a contradiction.
  • $$( p \rightarrow q ) \leftrightarrow ( \sim q \rightarrow \sim p )$$ is a contradiction
  • $$\sim ( \sim p ) \leftrightarrow p$$ is a tautology
  • $$p \vee ( \sim p )$$ is a tautology
Consider the following statements
$$P:$$Suman is brilliant
$$Q:$$Suman is rich
$$R:$$Suman is honest.
The negative of the statement."Suman is brilliant and dishonest, if and only if Suman is rich" can be expressed as
  • $$\sim [Q \leftrightarrow (P \wedge \sim R)]$$
  • $$\sim Q \leftrightarrow P \wedge R$$
  • $$\sim (P \wedge \sim R) \leftrightarrow Q $$
  • $$\sim P \wedge (Q \leftrightarrow \sim R)$$
Consider the following two statements: $$P:$$ if $$7$$ is an odd number, then $$7$$ is divisible by $$2$$.$$Q:$$ if $$7$$ is a prime number, then $$7$$ is an odd number If $$V_{1}$$ is the truth value of the contrapositive of $$P$$ and $$V_{2}$$ is the truth value of contrapositive of $$Q$$. Then the ordered pair $$\left(V_{1},V_{2}\right)$$ equals:
  • $$\left(F,F\right)$$
  • $$\left(T,T\right)$$
  • $$\left(F,T\right)$$
  • $$\left(T,F\right)$$
Negation of $$p \to \left( {p \vee  \sim q} \right)$$ is
  • $$( \sim p) \to ( \sim p \vee q)$$
  • $$p \wedge ( \sim p \wedge q)$$
  • $$\left( { \sim p} \right) \vee \left( { \sim p \vee \sim q} \right)$$
  • $$\left( { \sim p} \right) \leftarrow \left( { \sim p \to q} \right)$$
If $$(p\wedge \sim q)\wedge (p\wedge r)\rightarrow \vee \sim p \vee q$$ is false then the truth values of $$p,q$$ and $$r$$ are respectively
  • $$F,T,F$$
  • $$T,F,T$$
  • $$F,F,F$$
  • $$T,T,T$$
Consider the following three statements:
P : 5 is a prime number.
Q : 7 is a factor of 192.
R : L.C.M. of 5 and 7 is 35.
Then the truth value of which one of thefollowing statements is true ?
  • $$(P \wedge Q)\vee (\sim R)$$
  • $$(\sim P)\wedge (\sim Q \wedge R)$$
  • $$(\sim P) \vee (Q\wedge R)$$
  • $$P\vee (\sim Q \wedge R)$$
State whether the statement
P: "if x is a real number such that $$x^3+2x=0$$, then $$x$$ is $$0$$"  is true/false
  • True
  • False
Which of the following is not a tautology?
  • $$p\rightarrow (p\vee q)$$
  • $$(p\wedge q)\rightarrow p$$
  • $$(p\vee q)\rightarrow (p\wedge (\sim q))$$
  • $$(p\vee \sim p)$$
The negation of $$p\wedge \left( q \rightarrow\ r \right)$$ is
  • $$p\vee \left( \sim q\vee r \right)$$
  • $$\sim p\wedge \left( q\rightarrow r \right)$$
  • $$\sim p\wedge \left( \sim q\rightarrow\sim r \right)$$
  • $$\sim p\vee \left( q\wedge \sim r \right)$$
Which of the following is not true?
  • If the last column of its truth table contains only $$F$$ then it is a contradiction
  • Negation of a negation of a statement is the statement itself
  • If $$p$$ and $$q$$ are two statements then $$p \leftrightarrow q$$ is a tautology
  • If the last column of its truth table contains only $$T$$ then it is tautology
State whether the statement
P: "if x is a real number such that $$x^3+2x=0$$, then $$x$$ is $$0$$" is true/false.
  • True
  • False
Let $$p\rightarrow (\sim q\vee r)$$ is false, then truth values of p, q, r are respectively.
  • $$F, T, T$$
  • $$T, F, T$$
  • $$T, T, F$$
  • $$F, F, T$$
The negation of the boolean expression
$$\sim s\vee \left( \sim r\wedge s \right) $$ is equivalent to:
  • $$r$$
  • $$s\wedge r$$
  • $$s\vee r\quad $$
  • $$\sim s\wedge \sim r\quad $$
Determine whether the following compound statements are true or false:
Delhi is in India and $$2+2=4$$
  • True
  • False
Determine whether the following compound statements are true or false:
Delhi is in India and $$2+2=5$$
  • True
  • False
Determine whether the following compound statement are true of false:
Delhi is in England and $$2+2=4$$
  • True
  • False
Determine whether the following compound statements are true or false:
Delhi is in England and $$2+2=5$$
  • True
  • False
Check the validity of the following statement:
$$p:125$$ is a multiple of $$5$$ and $$7$$
  • True
  • False
State whether the statement
$$p:$$ If $$x$$ is a real number such that $$x^{3}+19x=0$$ , then $$x$$ is $$0$$ is true / False
  • True
  • False
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