1. Find the values of $$ x $$ and $$ y $$ if i) $$ (2 x+3, y-2)=(5,3) $$ (ii) $$ (x+3, y-2)=(y-1,2 x-3) $$. If the order pair $$ (p, 6) $$ and $$ (-4, q) $$ belong toR $$ =\{(x, y): 3 x+5 y=18\} $$, find the values of $$ p $$ and $$ q $$. 2. Let $$ A=\{2,3,4\} $$ and $$ B=\{1,2,3\} $$ be two sets. Find $$ A X B $$. And also find the relations from set $$ A $$ to set $$ B $$ satisfying the conditions (i) $$ x+y \leq 4 $$ (ii) $$ x=2 y $$. And represent these relations using arrow diagram and table.

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1. For problem 1, the solutions are: (i) $$ (x, y) = (1, 5) $$, (ii) $$ (x, y) = (5, 9) $$, and $$ p = -4, q = 6 $$. 2. For problem 2, the Cartesian product $$ A 	imes B $$ is \{(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)\}. The relations $$ R_1 $$ and $$ R_2 $$ are defined as $$ R_1 = \{(2, 1), (2, 2), (3, 1)\} $$ and $$ R_2 = \{(2, 1), (4, 2)\} $$, respectively. Arrow diagrams and tables are provided for both relations.

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