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

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

Options:

Correct Answer: Yes

Solution:

A relation R is reflexive if every element in set A is related to itself. Since R contains (1, 1), (2, 2), and (3, 3), R is reflexive.

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

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

Step 1: Identify the set A. In this case, A = {1, 2, 3}.
Step 2: Understand what a reflexive relation means. A relation R is reflexive if every element in set A is related to itself.
Step 3: Look at the relation R. Here, R = {(1, 1), (2, 2), (3, 3)}.
Step 4: Check if each element in set A is related to itself. We need to see if (1, 1), (2, 2), and (3, 3) are in R.
Step 5: Since (1, 1) is in R, 1 is related to itself.
Step 6: Since (2, 2) is in R, 2 is related to itself.
Step 7: Since (3, 3) is in R, 3 is related to itself.
Step 8: Since all elements in set A are related to themselves, we 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.