wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Which of the following is not logically equivalent to the proposition: “A real number is either rational or irrational”?


A

If a number is neither rational nor irrational then it is not real

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

If a number is not a rational or not an irrational, then it is not real

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

If a number is not real, then it is neither rational nor irrational

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

If a number is real, then it is rational or irrational

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

If a number is not a rational or not an irrational, then it is not real


Explanation for the correct options:

Rational number: A rational number is a number that can be expressed as the quotient or fraction pq of two integers, a numerator p and denominator q0.

Irrational number: All real numbers that aren't rational are referred to as irrational numbers.

Real numbers are a set of rational numbers and irrational numbers.

Logically incorrect statement is “If a number is not a rational or not an irrational, then it is not real”.

Because 2 is not a rational number but it is a real number.

Explanation for the incorrect options:

For option (a)

Given “If a number is neither rational nor irrational then it is not real”.

Since real numbers are a set of rational numbers and irrational numbers

Therefore, option (a) is the incorrect option.

For option (c)

Given “If a number is not real, then it is neither rational nor irrational”

Since real numbers are a set of rational numbers and irrational numbers

Therefore, option (c) is the incorrect option.
For option (d)

Given “If a number is real, then it is rational or irrational”

Since real numbers are a set of rational numbers and irrational numbers

Therefore, option (D) is the incorrect option.
Hence, the correct option is option (B).


flag
Suggest Corrections
thumbs-up
5
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Representing Irrational Number on Number Line
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon