If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R tr

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Question: If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R transitive?

Options:

Yes
No
Not enough information
None of the above

Correct Answer: No

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.

If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R tr

Practice Questions

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

Questions & Step-by-Step Solutions

If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R transitive?

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.

Transitive Relation – A relation R is transitive if for all a, b, c in A, whenever (a, b) and (b, c) are in R, then (a, c) must also be in R.

If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R tr

What’s inside this PDF?

If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R tr

Practice Questions

Questions & Step-by-Step Solutions

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