Answer to Question #236198 in Discrete Mathematics for dewatar

Question

Let set A = {1, 2, 3, 4} and B = {5, 6, 7, 8} whereby relation R₁ = {(a, b) | a = b - 1 } and R₂ = {(a, b) | a + b ≥ 3}. a is an element of set A and b is an element of set B. 

         

1. Write the relation for R₁ and R₂ where these represent the relation from set A to set B.      
2. Based on question in (1), solve R₁ – R₂ and R₂ – R₁                                                                                                  

Answer 1

1.

$R_1=\{(4,5)\}$

$R_2=\{(1,5),(1,6),(1,7),(1,8),(2.5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),$

$(4,5),(4,6),(4,7),(4,8)\}$

2.

$R_1-R_2=\{\empty\}$

$R_2-R_1=\{(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2.7),(2,8),(3,5),(3,6),(3,7),$

$(3,8),(4,6),(4,7),(4,8)\}$