Advertisement Remove all ads

Let a = (3, 5) and B = (7, 11). Let R = {(A, B) : a ∈ A, B ∈ B, a − B is Odd}. Show that R is an Empty Relation from a into B. - Mathematics

Let A = (3, 5) and B = (7, 11). Let R = {(ab) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.

Advertisement Remove all ads

Solution

Given:
A = (3, 5) and B = (7, 11)
Also,
R = {(ab) : a ∈ A, b ∈ B, a − b is odd}
a are the elements of A and b are the elements of B.

\[\therefore a - b = 3 - 7, 3 - 11, 5 - 7, 5 - 11\]
\[ \Rightarrow a - b = - 4, - 8, - 2, - 6\]
\[\text{ Here, a - b is always an even number}  .\]

So, R is an empty relation from A to B.
Hence proved.

Concept: Relation
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 2 Relations
Exercise 2.3 | Q 7 | Page 21
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×