Which transitivity requirement fails for R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4)} on A={1,2,3,4}?
Answer and explanation
Correct answer: (1,2) and (2,4) require (1,4)
Option A is correct because transitivity says that if (a,b) and (b,c) are in R, then (a,c) must also be in R. Here (1,2) and (2,4) are present, but (1,4) is absent. The other statements either use a pair that is not given or demand a conclusion unrelated to transitivity. Thus the relation fails the partial-order test specifically because transitivity fails.
Frequently asked questions
What is the correct answer to this question?
(1,2) and (2,4) require (1,4)
Why is this the correct answer?
Option A is correct because transitivity says that if (a,b) and (b,c) are in R, then (a,c) must also be in R. Here (1,2) and (2,4) are present, but (1,4) is absent. The other statements either use a pair that is not given or demand a conclusion unrelated to transitivity. Thus the relation fails the partial-order test specifically because transitivity fails.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
