Tran Lawson
10/10/2023 · Elementary School
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 \( A \times B \) 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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