Mathematics - Mathematical Reasoning
Exam Duration: 45 Mins Total Questions : 30
Which among the following is a statement?
- (a)
Close the door
- (b)
A square has all its unequal
- (c)
N is a natural number
- (d)
Please do me a favour
Which among the following is not a statement?
- (a)
where are you going?
- (b)
The sum of interior angles of a triangle is 2800
- (c)
12 is greater than 10.
- (d)
Every set is a finite set.
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
If \(p\leftrightarrow q\) is true, then which of the following is true?
- (a)
p is true and q is false
- (b)
p is false and q is true
- (c)
p is true and q is true
- (d)
None of the above
The value of ~(~p) is
- (a)
~p
- (b)
p~
- (c)
p
- (d)
q
\(\sim \left( p\vee q \right) \vee \left( \sim p\wedge q \right) \) is logically equivalent to
- (a)
~p
- (b)
p
- (c)
q
- (d)
nq
Which of the following is a statement?
- (a)
x is a real number
- (b)
Switch off the fan
- (c)
6 is a natural number
- (d)
Let me go
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
The statement 'If X2 is not even, then X is not even' is converse of the statement
- (a)
if x2 is odd, then x is even
- (b)
if x is not even, then x2 is even
- (c)
if x is even, then X2 is even
- (d)
if X is odd, then X2 is even
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)
\(p\wedge q\)
If p : Ajay works hard, q: Ajay gets good marks, then proposition \(\sim p\Rightarrow \sim q\) is equivalent to
- (a)
Ajay does not work hard and yet he gets good marks
- (b)
Ajay work hard if and only if he gets good marks
- (c)
If Ajay does not work hard, then he does not get good marks
- (d)
None of the above
The statement \(\sim (p\leftrightarrow \sim q)\) is
- (a)
equivalent to \(p\leftrightarrow q\)
- (b)
equivalent to \(\sim p\leftrightarrow q\)
- (c)
a tautology
- (d)
a fallacy
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
- (a)
\(\sim (Q\leftrightarrow (P\wedge \sim R)\)
- (b)
\(\sim Q\leftrightarrow P\wedge R\)
- (c)
\(\sim (P\wedge \sim R)\leftrightarrow Q\)
- (d)
\(\sim P\wedge (Q\leftrightarrow \sim R)\)
Which of the following is not a statement?
- (a)
Two plus three is seven
- (b)
A triangle has four sides
- (c)
Have you ever been to Delhi?
- (d)
5 is an odd number
The negation is given in (ii) of each of the following conjunctions given in (i).Which one is not CORRECT?
- (a)
(i) Delhi is in India and London is in England.
(ii) Delhi is not in India or London is not in England. - (b)
(i) 3 + 7 = 10 and 9 < 12.
(ii) 3 + 7 ≠10. 10 or 9 ∡12. - (c)
(i) Ram is honest or Kailash is dishonest.
(ii) Ram is not honest and Kailash is not dishonest. - (d)
(i) 19> l3 or 12 < 15.
(ii) 19 ⊁ 13 or 12 ∡ 15.
Which of the following statements is false?(a) The component statements are
p: J2 is a rational number.
q: fi. is an irrational number.
Here, we know that the first statement is false and the
second is true and "Or" is exclusive, so the compound
statement is true.
(b) The component statements are
p :To get into a public library, children need an identity card.
q :To get into a public library, children need a letter from
the school authorities.
Children can enter the library if they have either of the
two, an identity card or the letter, as well as when they
have both. Therefore, it is inclusive "Or". The compound
statement is also true.
(c) Here "Or" is exclusive. When we look at the
component statements, we get that the statement is true.
(d) p: Pune is the capital of Kolkata.
q : Pune is the capital of Karnataka.
Both these statements are false. So compound statement
is also false.
- (a)
\(\sqrt{2}\) is a rational number or an irrational number
- (b)
To enter into a public library children need an identity card from the school or a letter from the school authorities
- (c)
A rectangle is a quadrilateral or a 5-sided polygon
- (d)
Pune is a capital of Karnataka or Kolkata
Let p be the statement 'Ravi races' and let q be the statement 'Ravi wins'. Then the verbal translation of ~(p v (~ q)) is
- (a)
Ravi does not race and Ravi does not win
- (b)
It is not true that Ravi races and that Ravi does not win
- (c)
Ravi does not race or Ravi wins
- (d)
It is not true that Ravi races or that Ravi does not win
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 a number n is even, then n2 is even
- (a)
If a number n2 is odd, then n is not even
- (b)
If a number n2 is even, then n is odd
- (c)
If a number n2 is even, then n is even
- (d)
If a number n is odd, then n2 is odd
The conditional statement of "You will get a sweet dish after the dinner" is
- (a)
If you take the dinner, then you will get a sweet dish
- (b)
If you take the dinner, you will get a sweet dish
- (c)
You get a sweet dish if and only ifyou take the dinner
- (d)
None of these
Which of the following is not true?
- (a)
~(P ∧ q) = (~p) v (~q)
- (b)
~ (p v q) = (~ p) ∧ (~ q)
- (c)
p ⟶ q = ~ p v q
- (d)
~ (p v q) = ~ p v ~ q
Which of the following is not logically equivalent?
- (a)
~(p⟶q) and ((p ∧ ~q)
- (b)
~ (p v q) and (~ p) ∧ (~ q)
- (c)
p ⟶ q and (~p) ∧ q
- (d)
~[pv(~q)] and (~p) ∧ q
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
The negation of the statement "Rajesh or Rajni lived in Bangalore" is
- (a)
Rajesh did not live in Bangalore or Rajni lives in Bangalore
- (b)
Rajesh lives in Bangalore and Rajni did not live in Bangalore.
- (c)
Rajesh did not live in Bagalore and Rajni did not live in Bangalore
- (d)
Rajesh did not live in Bangalore or Rajni did not live in Bangalor
The negation of the statement "101 is not a multiple of 3" is
- (a)
101 is a multiple of 3
- (b)
101 is a multiple of 2
- (c)
101 is an odd number
- (d)
101 is an even number
The contrapositive of the statement
"If 7 is greater than 5, then 8 is greater than 6" is
- (a)
If 8 is greater than 6, then 7 is greater than 5
- (b)
If 8 not greater than 6, then 7 is greater than 5
- (c)
If 8 is not greater than 6, then 7 is not greater than 5
- (d)
If 8 is greater than 6, then 7 is not greater than 5
The converse of the statement
"If x > y, then x + a > y + a" is
- (a)
If x < y, then x + a < y + a
- (b)
If x + a > y + a, then x > y
- (c)
If x < y, then x + a > y + a
- (d)
If x > y, then x + a < y + a
Which of the following statement is a conjunction?
- (a)
Ram and Shyam are friends
- (b)
Both Ram and Shyam are tall
- (c)
Both Ram and Shyam are enemies
- (d)
None of these
Statement-I: The negation of the statement "I become a teacher, then I will open a school" is I will become a teacher and I will not open a school.
Statement-II: A statement which is formed by changing the truth value of a given statement by using word like 'no' or 'not' is called negation of the given statement.
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement-I
- (b)
If both Statement-I and Statement-II are true and Statement-II is not the correct explanation of Statement-I
- (c)
If Statement-I is true but Statement-II is false
- (d)
If Statement-I is true but Statement-II is true.