IISER Mathematics - Mathematical Reasoning
Exam Duration: 45 Mins Total Questions : 30
Which among the following is not a conjunction?
- (a)
Gautam and Rahul are good friends
- (b)
The earth is round and the Sun is hot
- (c)
9>4and12>15
- (d)
None of the above
The value of~(~p) is
- (a)
~p
- (b)
p~
- (c)
p
- (d)
q
Which of the following is not equivalent to\(p\leftrightarrow q\) ?
- (a)
p if and only if q
- (b)
p is necessary and sufficient for q
- (c)
q if and only if p
- (d)
None of the above
Which among the following is not a statement?
- (a)
Where are you going?
- (b)
The sum of interior angles of a triangle is 280o .
- (c)
12 is greater than 10.
- (d)
Every set is a finite set.
Which among the following is a conjunction?
- (a)
12 + 12 = 24 or 12 is greater than 10
- (b)
India is in Asia or Lucknow is in UP
- (c)
2 + 2 = 4 and 12 is greater than 10
- (d)
None of the above
Choose disjunction among the following sentences.
- (a)
It is raining and the Sun is shining
- (b)
Ram and Shyam are good friends
- (c)
2 or 3 is a prime number
- (d)
Everyone who lies in India is an Indian
If p : Samir is tall, q : Samir is intelligent, then \(\sim p\vee q\) means
- (a)
Samir is not tall or he is intelligent
- (b)
Samir is tall or he is intelligent
- (c)
Samir is not tall and he is intelligent
- (d)
Samir is not tall, so he is intelligent
If p.q and r are simple propositions with truth values T, F, T respectively, then the truth value of \(\left( \sim p\vee q \right) \wedge \sim q\rightarrow p\) is
- (a)
true
- (b)
false
- (c)
true, if r is false
- (d)
None of the above
\(\sim r\wedge s\) is equivalent to
- (a)
\(r\rightarrow s\)
- (b)
∼(s\(\rightarrow \)r)
- (c)
s\(\rightarrow \)r
- (d)
∼(r\(\rightarrow \)s)
Which of the following is logically equivalent to ∼(p\(\rightarrow \)q)?
- (a)
\(\sim p\wedge \sim q\)
- (b)
\(\sim p\wedge q\)
- (c)
\(p\wedge \sim q\)
- (d)
\(p\wedge q\)
Among the following statements, which is a tautology?
- (a)
\(p\wedge (p\vee q)\)
- (b)
\(p\vee (p\wedge q)\)
- (c)
\([p\wedge (p\rightarrow q)]\rightarrow q\)
- (d)
\(q\rightarrow [p\wedge (p\rightarrow q)]\)
Which of the following is true for any two statements p and q?
- (a)
\(\sim [p\vee \sim q]\equiv \sim p\wedge q\)
- (b)
\(\sim p\wedge q\) is a fallacy
- (c)
\(p\vee \sim q\) is a tautology
- (d)
\(p\vee \sim q\) is a contradiction
Which of the following sentences is not a statement?
- (a)
9 is less than 7
- (b)
The sun is a star
- (c)
There is no rain without clouds
- (d)
Mathematics is fun
The sentence "There are 35 days in a month" is
- (a)
a statement
- (b)
not a statement
- (c)
may be a statement or not
- (d)
None of the above
Which of the following sentences is a statement?
- (a)
5 is less than 7
- (b)
Where are you going?
- (c)
Close the door
- (d)
How funny he is!
Which of the following is a statement?
- (a)
Please help me
- (b)
Hurrah! India has won the match
- (c)
Good night to all
- (d)
17 is a prime number
Which one of the following statements is not a false statement?
- (a)
p: Each radius of a circle is a chord of the circle
- (b)
q: Cricle is a particular case of an ellipse
- (c)
r: \(\sqrt{13}\) is a rational number
- (d)
s: The centre of a circle bisects each chord of the circle
Which of the following statements is false after writing the component statements for each of the following statement?
- (a)
The sky is blue and the grass is green
- (b)
Sun rises in the east and sun sets in the west
- (c)
126 is a multiple of 11 and 17
- (d)
A quadrilateral has four sides and sum of the angles of quadrilateral is 360°
If p: It is snowing, q : I am cold, then the compound statement "It is snowing and it is not that I am cold" is given by
- (a)
p\(\wedge \)(~q)
- (b)
p \(\wedge \) q
- (c)
(~p)\(\wedge \)q
- (d)
(~p)\(\wedge \)(~q)
If P: The earth is round, q: 3 + 4 = 7,then (~p) v (~q) is
- (a)
It is not that the earth is round or 3 + 4 = 7
- (b)
The earth is round and 3 + 4 = 7
- (c)
It is not that the earth is round or it is not that 3 + 4 = 7
- (d)
The earth is round or 3 + 4 = 7
If S(p, q, r) = (~ p) v [~ (q ∧ r)] is a compound statement, then S(~p, ~q. ~r) is
- (a)
~S(p, q, r)
- (b)
S(p, q, r)
- (c)
p v (q ∧ r)
- (d)
p v (q v r)
Write the contrapositive of the following statement:
If you are born in India, then you are a citizen of India
- (a)
If you are not a citizen ofIndia, then you were not born in India
- (b)
If you are citizen of India, then you were born in India
- (c)
If you are not a citizen ofIndia, you were born in India
- (d)
If you are born in India, then you are not a citizen of India
Write the converse of the following statement.
If two integers a and b are such that a > b, then a - b is always a positive integer.
- (a)
If two integers a and b are such that a < b, then a - b is always positive integer
- (b)
If a < b, then a - b is always a negative integer
- (c)
If two integers a and b are such that a > b, then a - b is not a positive integer
- (d)
If two integers a and b are such that a - b is always a positive integer, then a > b
Which of the following statements is valid?
Statement-I: 125 is divisible by 5 and 7.
Statement-II: 131 is a multiple of 3 or 11.
- (a)
Only Statement-I
- (b)
Only Statement-II
- (c)
Both Staternent-I and Staternent-II
- (d)
Neither Statement-I nor Staternent-II
If the truth values of p, q and rare T, F and F respectively, then the compound proposition whose truth value is false, is
- (a)
(p ∧ q) V r
- (b)
(p ⟶ q) ⟶r
- (c)
(~p v q) ↔️ r
- (d)
~p v(q ⟶ r)
Consider the following statements:
(i) If price increases, then demand falls.
(ii) If price does not increase, then demand does not fall.
(iii)If demand falls, then price does not increase.
(iv) If demand does not fall, then price does not increase. Identify the pair of statement having the same meaning.
- (a)
(i) and (iv)
- (b)
(i) and (ii)
- (c)
(ii) and (iii)
- (d)
None of these
Let p : Rahul has physical disability.
q : Rahul stood first in the class.
Then the compound statement 'Inspite of physical disability, Rahul stood first in the class' is
- (a)
p ∧ - q
- (b)
p ∧ q
- (c)
~ P ∧ q
- (d)
~ (p ∧ q)
Which of the following is not a statement?
- (a)
Smoking is injurious to health
- (b)
2 + 2 = 4
- (c)
2 is the only even prime number
- (d)
Come here
The converse of the statement
"If sun is not shining, then sky is filled with clouds" is
- (a)
If sky is filled with clouds, then the sun is not shining
- (b)
If sun is shining, then sky is filled with clouds.
- (c)
If sky is clear, then sun is shining
- (d)
If sun is not shining, then sky is not filled with clouds
Which of the following is the conditional of p ? q?
- (a)
q is sufficient for p
- (b)
p is necessary for q
- (c)
p only if q
- (d)
if q, then p