Falling Behind in Studies? Join Our Performance Improvement Batch. Enroll For Free
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Live 1-1 coding classes to unleash the creator in your Child
Chapter 31: Mathematical Reasoning – Exercise 31.2 Mathematical Reasoning – Exercise – 31.2 – Q.1 The negation of the statement: Banglore is the capital of Karnataka. is Banglore is not the capital of Karnataka. The negation of the statement: It rained on July 4,2005. is It did not rain on July 4, 2005. The negation of the statement: Ravish is honest. is Ravish is not honest. The negation of the statement: The earth is round. is The earth is not round. The negation of the statement: The sun is cold. is The sun is not cold. Mathematical Reasoning – Exercise – 31.2 – Q.2 The negation of the statements: All birds sing. is Not all birds sing. The negation of the statements: Some even integers are prime. is No even integers is prime. The negation of the statements: There is a complex number which is not a real number. is All complex numbers are real numbers. The negation of the statements: I will not go to school. is I will go to school. The negation of the statements: Both the diagonals of a rectangle have the same length. is There is at least one rectangle whose both diagonals do not have the same length. The negation of the statements: All policemen are thieves. is No policemen is thief. Mathematical Reasoning – Exercise – 31.2 – Q.3 (i) The number x is not a rational number. ⇒ The number x is an irrational number. ∴ The statement “The number x is not an irrational number." is a negation of the first statement. (ii) The number x is not a rational number. ⇒ The number x is an irrational number. The statement "The number x is an irrational number” is not a negation of the first statement. Mathematical Reasoning – Exercise – 31.2 – Q.4 (i) The negation of the statement: p: For every positive real number x, the number (x -1) is also positive. is ~p: There exists a positive real number x such that the number (x - 1) is not positive. (ii) The negation of the statement: q: For every real number x, either x > 1 or x < 1. is ~q: There exists a real number such that neither x > 1 or x <1. (iii) The negation of the statement: r: There are exists a number x such that 0 < x <1. is ~r: For every real number x, either x ≤ or x ≥ al. Mathematical Reasoning – Exercise – 31.2 – Q.5 The negation of the statement: a + b = b + a is true for every real number a and b. is There exist real numbers a and b for which a + b ≠ b + a. So, the given statement is not the negation of the first statement.
The negation of the statement:
Banglore is the capital of Karnataka.
is
Banglore is not the capital of Karnataka.
It rained on July 4,2005.
It did not rain on July 4, 2005.
Ravish is honest.
Ravish is not honest.
The earth is round.
The earth is not round.
The sun is cold.
The sun is not cold.
The negation of the statements:
All birds sing.
Not all birds sing.
Some even integers are prime.
No even integers is prime.
There is a complex number which is not a real number.
All complex numbers are real numbers.
I will not go to school.
I will go to school.
Both the diagonals of a rectangle have the same length.
There is at least one rectangle whose both diagonals do not have the same length.
All policemen are thieves.
No policemen is thief.
(i) The number x is not a rational number.
⇒ The number x is an irrational number.
∴ The statement “The number x is not an irrational number." is a negation of the first statement.
(ii) The number x is not a rational number.
The statement "The number x is an irrational number” is not a negation of the first statement.
(i)
p: For every positive real number x, the number (x -1) is also positive.
~p: There exists a positive real number x such that the number (x - 1) is not positive.
(ii)
q: For every real number x, either x > 1 or x < 1.
~q: There exists a real number such that neither x > 1 or x <1.
(iii)
r: There are exists a number x such that 0 < x <1.
~r: For every real number x, either x ≤ or x ≥ al.
a + b = b + a is true for every real number a and b.
There exist real numbers a and b for which a + b ≠ b + a.
So, the given statement is not the negation of the first statement.
Signing up with Facebook allows you to connect with friends and classmates already using askIItians. It’s an easier way as well. “Relax, we won’t flood your facebook news feed!”
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
Chapter 31: Mathematical Reasoning –...
