Determine if the relation R = (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,3), (4,1) on the set A = 1, 2, 3, 4 is reflexive, symmetric, or transitive.

Step 1: Check for Reflexivity. A relation R on a set A is reflexive if for every element a A, the pair (a, a) is in R. The set is A = \1, 2, 3, 4\. For R to be reflexive, it must contain (1,1), (2,2), (3,3), (4,4). Given R = \(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,3), (4,1)\. We observe that (4,4) is not in R. Therefore, R is not reflexive. Step 2: Check for Symmetry. A relation R on a set A is symmetric if for every pair (a, b) R, the pair (b, a) is also in R. Let's check the pairs in R: • (1,2) R, and (2,1) R. This part is symmetric. • (1,3) R. For R to be symmetric, (3,1) must also be in R. However, (3,1) is not in R. Therefore, R is not symmetric. Step 3: Check for Transitivity. A relation R on a set A is transitive if for every a, b, c A, if (a, b) R and (b, c) R, then (a, c) must also be in R. Let's check for a counterexample: • Consider (4,1) R and (1,2) R. For R to be transitive, (4,2) must be in R. However, (4,2) is not in R. Therefore, R is not transitive. Step 4: Conclude the properties of R. Based on the checks, the relation R is not reflexive, not symmetric, and not transitive. Step 5: Select the correct option. Comparing our findings with the given options: (A) R is not reflexive but symmetric - Incorrect (not symmetric) (B) R is reflexive but not transitive - Incorrect (not reflexive) (C) R is neither reflexive, nor symmetric, nor transitive - Correct (D) Equivalence Relation - Incorrect (an equivalence relation must be reflexive, symmetric, and transitive) The final answer is C Last free one today — make it count tomorrow, or type /upgrade for unlimited.