Mathematics - Mathematical Reasoning
Exam Duration: 45 Mins Total Questions : 30
Which of the following is wrong form of 'if p, then q'?
- (a)
p is sufficient condition for q
- (b)
p only if q
- (c)
q is necessary condition for p
- (d)
~q\(\rightarrow\)p
~(p v q)v(~p^q) is logically equivalent to
- (a)
~p
- (b)
p
- (c)
q
- (d)
nq
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
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 > 4 and 12 > 15
- (d)
None of the above
Which among the following is not a negation of 'The Sun is a star'?
- (a)
The Sun is not a star.
- (b)
It is not the case that Sun is a star.
- (c)
It is false that the Sun is a star.
- (d)
It is true that the Sun is a star.
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
Match the terms of column I with the terms of column II and choose the correct option from the codes given below.
Column I | Column II | ||
A. | p: Each radius of a circle is a chord of the circle. | p. | True |
B. | q: The center of a circle bisects each chord of the circle | q. | False |
C. | r: Circle is a particular case of an ellipse. | ||
D. | s: If x and y are integers such that x > y, then -x<-y. | ||
E. | t: \(\sqrt { 11 } \) is a rational number. |
- (a)
A B C D E p q p q p - (b)
A B C D E p p q p q - (c)
A B C D E q q p p q - (d)
A B C D E q p q q p
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
Which among the following is false?
- (a)
\(\sqrt { 6 } \) is a rational number or an irrational number
- (b)
A square is a quadrilateral or a 6 sided polygon
- (c)
Mumbai is the capital of Kolkata or karnataka
- (d)
The school is closed, if there is a holiday or Sunday
The negation of the statement 'If I become a teacher, then I will open a school', is
- (a)
The negation of the statement 'If I become a teacher, then I will open a school', is
- (b)
Neither I will become a teacher nor I will open a school
- (c)
I will not become a teacher or I will open a school
- (d)
I will become a teacher and I will not open a school
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
Which of the following sentences is not a statement?
- (a)
Two plus three is ten
- (b)
Every square is a triangle
- (c)
Sun rises in the East
- (d)
Everyone in this room is bold
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°
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.
"It is raining and weather is cold." The negation of the statement is
- (a)
It is not raining and weather is cold
- (b)
It is raining or weather is not cold
- (c)
It is not raining or weather is not cold
- (d)
It is not raining and weather is not cold
Which of the following statements is "inclusive or" statement?
- (a)
Sun rises or moon sets
- (b)
All integers are positive or negative
- (c)
Two lines intersect at a point or are parallel
- (d)
The school is closed if it is holiday or a Sunday
Which of the following statements is exclusive "Or" statement?
- (a)
To enter in a country, you need a passport or a voter registration card
- (b)
The school is closed if it is a holiday or a Sunday
- (c)
Two lines intersect at a point or are parallel
- (d)
Candidate who has cleared P-TET or C-TET is eligible for teaching
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
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
The statement ~ p v ~ q is equivalent to
- (a)
~ q v p
- (b)
~ (p ៱ q)
- (c)
P ៱ ~ q
- (d)
q v p
The contrapositive and converse of the statement : "If the two lines are parallel, then they do not interest in the same plane" is
- (a)
If the two straight lines intersect in a plane, the the lines are not parallel.
If the two lines do not intersect in the same plane, then the two lines are parallel - (b)
If the two straight lines do not intersect in a plane, then the lines are parallel.
If the two lines do not intersect in the same plane, then the two lines are parallel - (c)
If the two straight lines intersect in a plane, then the lines are not parallel.
If the two lines do not intersect in the same plane, then the two lines are not parallel. - (d)
None of these
Which of the following is different from the others?
- (a)
~(p↔️q)
- (b)
~p ↔️ q
- (c)
p ↔️ ~q
- (d)
None of these
The negation of the statement "72 is divisible by 2 and 3" is
- (a)
72 is not divisible by 2 or 72 is not divisible by 3
- (b)
72 is not divisible by 2 and 72 is not divisible by 3
- (c)
72 is divisible by 2 and 72 is not divisible by 3
- (d)
72 is not divisible by 2 and 72 is divisible by 3
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
The negation of the statement "The product of 3 and 4 is 9" is
- (a)
It is false that the product of 3 and 4 is 9
- (b)
The product of 3 and 4 is 12
- (c)
The product of 3 and 4 is not 12
- (d)
It is false that the product of 3 and 4 is not 9
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