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

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

Options:

Correct Answer: Yes

Solution:

A relation is reflexive if every element in the set is related to itself. Here, R includes (1, 1), (2, 2), and (3, 3), so R is reflexive.

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

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

Correct Answer: Yes, R is reflexive.

Step 1: Identify the set A. Here, A = {1, 2, 3}.
Step 2: Understand what a reflexive relation means. A relation is reflexive if every element in the set is related to itself.
Step 3: Check the relation R. The relation R is given as R = {(1, 1), (2, 2), (3, 3)}.
Step 4: Look at each element in set A. The elements are 1, 2, and 3.
Step 5: Verify if each element is related to itself. We see (1, 1), (2, 2), and (3, 3) in R.
Step 6: Since all elements (1, 2, and 3) are related to themselves, conclude that R is 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.