If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R transitive?
Practice Questions
1 question
Q1
If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R transitive?
Yes
No
Not enough information
None of the above
A relation R is transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) must also be in R. Here, (1, 2) and (2, 3) are in R, but (1, 3) is not, so R is not transitive.
Questions & Step-by-step Solutions
1 item
Q
Q: If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R transitive?
Solution: A relation R is transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) must also be in R. Here, (1, 2) and (2, 3) are in R, but (1, 3) is not, so R is not transitive.
Steps: 6
Step 1: Identify the set A, which is {1, 2, 3}.
Step 2: Identify the relation R, which is {(1, 2), (2, 3)}.
Step 3: Understand the definition of transitive: A relation R is transitive if whenever (a, b) is in R and (b, c) is in R, then (a, c) must also be in R.
Step 4: Look for pairs in R: We have (1, 2) and (2, 3). Here, 'b' is 2.
Step 5: Check if (1, 3) is in R: Since (1, 3) is not in R, we need to conclude.
Step 6: Since (1, 2) and (2, 3) are in R but (1, 3) is not, R is not transitive.
