Let A= {2, 3, 5, 7, 9}. Let R be the relation on A defined by x R y if and only if $$2x\leq3y$$. Let l be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then l + m is equal to:

Given $$A = \{2, 3, 5, 7, 9\}$$ and $$xRy$$ iff $$2x \leq 3y$$.

For $$x = 2$$ we have $$4 \leq 3y$$ which gives $$y \geq 4/3$$, so $$y \in \{2, 3, 5, 7, 9\}$$, giving 5 pairs.

For $$x = 3$$ we have $$6 \leq 3y$$ which gives $$y \geq 2$$, so $$y \in \{2, 3, 5, 7, 9\}$$, giving 5 pairs.

For $$x = 5$$ we have $$10 \leq 3y$$ which gives $$y \geq 10/3$$, so $$y \in \{5, 7, 9\}$$, giving 3 pairs.

For $$x = 7$$ we have $$14 \leq 3y$$ which gives $$y \geq 14/3 \approx 4.67$$, so $$y \in \{5, 7, 9\}$$, giving 3 pairs.

For $$x = 9$$ we have $$18 \leq 3y$$ which gives $$y \geq 6$$, so $$y \in \{7, 9\}$$, giving 2 pairs.

Thus the total number of pairs in $$R$$ is $$l = 5 + 5 + 3 + 3 + 2 = 18$$.

Since symmetry requires that if $$(x,y) \in R$$ then $$(y,x)$$ must also be in $$R$$, we check each pair and its reverse:

$$(2,2) \in R$$ so $$(2,2) \in R$$ which is already symmetric.

$$(2,3) \in R$$ and $$6 \leq 6$$ shows $$(3,2) \in R$$.

$$(2,5) \in R$$ but $$10 \leq 6$$ is false, so we add $$(5,2)$$.

$$(2,7) \in R$$ but $$14 \leq 6$$ is false, so we add $$(7,2)$$.

$$(2,9) \in R$$ but $$18 \leq 6$$ is false, so we add $$(9,2)$$.

$$(3,2) \in R$$ is already handled.

$$(3,3) \in R$$ shows $$(3,3) \in R$$.

$$(3,5) \in R$$ but $$10 \leq 9$$ is false, so we add $$(5,3)$$.

$$(3,7) \in R$$ but $$14 \leq 9$$ is false, so we add $$(7,3)$$.

$$(3,9) \in R$$ but $$18 \leq 9$$ is false, so we add $$(9,3)$$.

$$(5,5) \in R$$ is symmetric.

$$(5,7) \in R$$ and $$14 \leq 15$$ shows $$(7,5) \in R$$.

$$(5,9) \in R$$ but $$18 \leq 15$$ is false, so we add $$(9,5)$$.

$$(7,5) \in R$$ is already handled.

$$(7,7) \in R$$ is symmetric.

$$(7,9) \in R$$ and $$18 \leq 21$$ shows $$(9,7) \in R$$.

$$(9,7) \in R$$ is already handled.

$$(9,9) \in R$$ is symmetric.

The elements that must be added to make the relation symmetric are $$(5,2), (7,2), (9,2), (5,3), (7,3), (9,3), (9,5)$$, giving $$m = 7$$.

$$l + m = 18 + 7 = 25$$

The answer is Option 2: 25.