31. If $$p$$ and $$q$$ are two statement then $$\left( {p \leftrightarrow \, \sim q} \right)$$ is true when -
A
$$p$$ and $$q$$ both are true
B
$$p$$ and $$q$$ both are false
C
$$p$$ is false and $$q$$ is true
D
None of these
Answer :
$$p$$ is false and $$q$$ is true
32. If $$p :$$ Raju is tall and $$q :$$ Raju is intelligent, then the symbolic statement $${ \sim p \vee q}$$ means
A
Raju is not tall or he is intelligent
B
Raju is tall or he is intelligent
C
Raju is not tall and he is intelligent
D
Raju is not tall implies he is intelligent
Answer :
Raju is not tall or he is intelligent
33. Which of the following is false ?
A
$$p \vee \sim p\,$$ is a tautology
B
$$ \sim \left( { \sim p} \right) \leftrightarrow p\,$$ is a tautology
C
$$p \wedge \sim p\,$$ is a contradiction
D
$$\left( {\left( {p \wedge q} \right) \to q} \right) \to p\,$$ is a tautology
Answer :
$$\left( {\left( {p \wedge q} \right) \to q} \right) \to p\,$$ is a tautology
34. The inverse of the statement, ' If $$x$$ is zero then we cannot divide by $$x$$' is
A
If we cannot divide by $$x$$, then $$x$$ is zero
B
If we cannot divide by $$x$$, then $$x$$ is not zero
C
If $$x$$ is not zero then we divide by $$x$$
D
None
Answer :
If $$x$$ is not zero then we divide by $$x$$
35. The following statement $$\left( {p \to q} \right) \to \left[ {\left( { \sim p \to q} \right) \to q} \right]$$ is:
A
a fallacy
B
a toutology
C
equivalent to $${ \sim p \to q}$$
D
equivalent to $${ p \to \sim q}$$
Answer :
a toutology
36. $$ \sim \left( {p \Rightarrow q} \right) \Leftrightarrow \, \sim p \vee \sim q{\text{ is}}$$
A
A tautology
B
A contradiction
C
Neither a tautology nor a contradiction
D
Cannot come to any conclusion
Answer :
Neither a tautology nor a contradiction
37.
The negation of the statement
"If I become a teacher, then I will open a school", is:
A
I will become a teacher and I will not open a school.
B
Either I will not become a teacher or I will not open a
school.
C
Neither I will become a teacher nor I will open a school.
D
I will not become a teacher or I will open a school.
Answer :
I will become a teacher and I will not open a school.
38. The contrapositive of $$p \to \left( { \sim q \to \, \sim r} \right)$$ is -
A
$$\left( { \sim q \wedge r} \right) \to \, \sim p$$
B
$$\left( { q \to r} \right) \to \, \sim p$$
C
$$\left( {q \, \vee \sim r} \right) \to \, \sim p$$
D
None of these
Answer :
$$\left( { \sim q \wedge r} \right) \to \, \sim p$$
39. Identify the false statements
A
$$ \sim \left[ {p \vee \left( { \sim q} \right)} \right] \equiv \left( { \sim p} \right) \vee q$$
B
$$\left[ {p \vee q} \right] \vee \left( { \sim p} \right)$$ is a tautology
C
$$\left[ {p \wedge q} \right] \wedge \left( { \sim p} \right)\,$$ is a contradiction
D
$$ \sim \left[ {p \vee q} \right] \equiv \left( { \sim p} \right) \vee \left( { \sim q} \right)$$
Answer :
$$ \sim \left[ {p \vee q} \right] \equiv \left( { \sim p} \right) \vee \left( { \sim q} \right)$$
40.
If $$p :$$ Ashok works hard
$$q :$$ Ashok gets good grade
The verbal form for $$\left( { \sim p \to q} \right)$$ is
A
If Ashok works hard then gets good grade
B
If Ashok does not work hard then he gets good grade
C
If Ashok does not work hard then he does not get good grade
D
Ashok works hard if and only if he gets grade
Answer :
If Ashok does not work hard then he gets good grade