Determine which of the following are reflexive relations on set $A=(1,2,3\}$.

1. $R_1=\left(\right(1,1),(2,2),(3,3),(2,1\left)\right\}$
2. $R_2=\left(\right(1,1),(3,3),(2,1),(3,2\left)\right\}$.

If $R_1$ is reflexive then answer $1$ and if $R_2$ is reflexive then answer $2$.

Q. Let $R_1$ and $R_2$ be two relations defined on a non empty set A. Which of the following statements is false? Give reasons in support of your answer.
(a) If $R_1$ and $R_2$ are reflexive, then so is $R_1\cap R_2$
(b) If $R_1$ and $R_2$ are symmetric, then so is $R_1\cup R_2$
(c) If $R_1$ and $R_2$ are transitive, then so is $R_1\cup R_2$
(d) If $R_1$ and $R_2$ are transitive, then so is $R_1\cap R_2$
(e) If $R_1$ and $R_2$ are symmetric, then so is $R_1\cap R_2$

Q. Let $A=\{1,2,3\}$ and let

Q. Let A = {1, 2, 3}, and let R₁ = {(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)}, R₂ = {(2, 2), (3, 1), (1, 3)}, R₃ = {(1, 3), (3, 3)}. Find whether or not each of the relations R₁, R₂, R₃ on A is (i) reflexive (ii) symmetric (iii) transitive.

Q. Test whether the following relations R₁, R₂, and R₃ are (i) reflexive (ii) symmetric and (iii) transitive:
(i) R₁ on Q₀ defined by (a, b) ∈ R₁ ⇔ a = 1/b.
(ii) R₂ on Z defined by (a, b) ∈ R₂ ⇔ |a – b| ≤ 5
(iii) R₃ on R defined by (a, b) ∈ R₃ ⇔ a² – 4ab + 3b² = 0.

Q. If $A=\{1,2,3\},$ then number of reflexive relations that can be defined on $A$ is