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Class 11 Maths
Mathematical Reasoning
Quiz 1
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The converse of the statement p ⇒ q is
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p ⇒ q
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q ⇒ p
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~p ⇒ q
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~q ⇒ p
Explanation
q ⇒ p
Hint:
The converse of the statement p ⇒ q is
q ⇒ p
Which of the following is not a statement
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The product of (-1) and 8 is 8
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All complex number are real number
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Today is windy day
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All of the above
Explanation
All of the above
Hint:
A sentence is a statement if it is true.
None of the above sentence is true.
So, option 4 is the correct answer.
If (p or q) is true, then
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p is true and q is false
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p is true and q is true
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p is false and q is true
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All of the above
Explanation
All of the above
Hint:
(p or q) is false when both p and q are false otherwise it is true.
Which of the following statement is a conjunction
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Ram and Shyam are friends
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Both Ram and Shyam are friends
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Both Ram and Shyam are enemies
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None of these
Explanation
None of these
Hint:
All the statements are conjunction. So, option 4 is the correct answer.
Which of the following is a compound statement
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Sun is a star
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I am a very strong boy
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There is something wrong in the room
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7 is both odd and prime number.
Explanation
7 is both odd and prime number.
Hint:
A compound statement is connected with And, or, etc.
So, the statement 7 is both odd and prime number is a compound statement.
Which of the following is true
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A prime number is either even or odd
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√3 is irrational number.
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24 is a multiple of 2, 4 and 8
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Everyone in India speaks Hindi.
Explanation
Everyone in India speaks Hindi.
Hint:
The statement Everyone in India speaks Hindi is not true.
This is because, there are some states like Tamilnadu, Kerala, etc. where the person does not speak Hindi.
The contra-positive of the statement If a triangle is not equilateral, it is not isosceles is
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If a triangle is not equilateral, it is not isosceles
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If a triangle is equilateral, it is not isosceles
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If a triangle is not equilateral, it is isosceles
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If a triangle is equilateral, it is isosceles
Explanation
If a triangle is equilateral, it is isosceles
Hint:
Given, statement is:
If a triangle is not equilateral, it is not isosceles.
Now, contra-positive is:
If a triangle is equilateral, it is isosceles.
The contra-positive of the statement if p then q is
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if ~p then q
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if p then ~q
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if q then p
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if ~q then ~p
Explanation
if ~q then ~p
Hint:
Given statement is if p then q
Now, contra-positive of the statement is:
if ~q then ~p
Which of the following is not a negation of the statement A natural number is greater than zero
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A natural number is not greater than zero
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It is false that a natural number is greater than zero
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It is false that a natural number is not greater than zero
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None of these
Explanation
It is false that a natural number is not greater than zero
Hint:
Gievn statement is:
A natural number is greater than zero
Negation of the statement:
A natural number is not greater than zero
It is false that a natural number is greater than zero
So, option 3 is not true.
Which of the following is a statement
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x is a real number
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Switch of the fan
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6 is a natural number
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Let me go
Explanation
6 is a natural number
Hint:
The statement 6 is a natural number is true.
So, it is a statement.
If (p and q) is false then
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p is true and q is false
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p is false and q is false
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p is false and q is true
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all of the above
Explanation
all of the above
Hint:
(p and q) is true when both p and q are true otherwise it is false.
The connective in the statement 2 + 7 > 9 or 2 + 7 < 9 is
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and
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or
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>
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<
Explanation
or
Hint:
Given, statement is 2 + 7 > 9 or 2 + 7 < 9 Here, connective is or. It connects two statement 2 + 7 > 9, 2 + 7 < 9
The negation of the statement The product of 3 and 4 is 9 is
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It is false that the product of 3 and 4 is 9
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The product of 3 and 4 is 12
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The product of 3 and 4 is not 12
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It is false that the product of 3 and 4 is not 9
Explanation
It is false that the product of 3 and 4 is 9
Hint:
Given, statement is The product of 3 and 4 is 9
The negation of the statement is:
It is false that the product of 3 and 4 is 9
The converse of the statement if a number is divisible by 10, then it is divisible by 5 is
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if a number is not divisible by 5, then it is not divisible by 10
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if a number is divisible by 5, then it is not divisible by 10
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if a number is not divisible by 5, then it is divisible by 10
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if a number is divisible by 5, then it is divisible by 10
Explanation
if a number is divisible by 5, then it is divisible by 10
Hint:
Given, statement is if a number is divisible by 10, then it is divisible by 5
Now, converse of the statement is:
if a number is divisible by 5, then it is divisible by 10
Which of the following is the conditional p → q
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q is sufficient for p
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p is necessary for q
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p only if q
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if q then p
Explanation
p only if q
Hint:
Given, p → q
Now, conditional of the statement is
p only if q
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