If the relation R on set A = {1, 2, 3} is defined as R = {(1, 2), (2, 3)}, is R

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Question: If the relation R on set A = {1, 2, 3} is defined as R = {(1, 2), (2, 3)}, is R reflexive?

Options:

Correct Answer: No

Solution:

A relation is reflexive if every element is related to itself. Here, (1,1), (2,2), and (3,3) are not in R, so R is not reflexive.

If the relation R on set A = {1, 2, 3} is defined as R = {(1, 2), (2, 3)}, is R reflexive?

If the relation R on set A = {1, 2, 3} is defined as R = {(1, 2), (2, 3)}, is R reflexive?

Correct Answer: No, R is not reflexive.

Step 1: Understand what a reflexive relation is. A relation is reflexive if every element in the set is related to itself.
Step 2: Identify the elements in set A. The set A is {1, 2, 3}.
Step 3: List the pairs that would show reflexivity. For set A, the pairs needed for reflexivity are (1, 1), (2, 2), and (3, 3).
Step 4: Check if these pairs are in the relation R. The relation R is {(1, 2), (2, 3)}.
Step 5: Look for (1, 1) in R. It is not there.
Step 6: Look for (2, 2) in R. It is not there.
Step 7: Look for (3, 3) in R. It is not there.
Step 8: Since none of the pairs (1, 1), (2, 2), or (3, 3) are in R, conclude that R is not reflexive.

Reflexive Relation – A relation R on a set A is reflexive if for every element a in A, the pair (a, a) is in R.