📘 discrete mathematics

1. The problem asks to identify properties of relation $$R = \{(1,2), (2,2), (1,1), (4,4), (1,3), (3,3), (3,2)\}$$ on set $$A=\{1,2,3,4\}$$. \nCheck reflexivity: Elements 1, 2, 3,

1. **Solve the recurrence relation** $a_n = 8a_{n-1} - 16a_{n-2}$ for $n\ge 2$ with $a_0=16, a_1=80$. 2. Write the characteristic equation: $$r^2 - 8r + 16 = 0$$

1. Problem (7a): Solve the recurrence relation $$a_n = 8a_{n-1} - 16a_{n-2}$$ for $$n \geq 2$$ with initial conditions $$a_0 = 16$$ and $$a_1 = 80$$. 2. Step 1: Characteristic equa

1. Problem: Solve the recurrence relation $a_n = 8a_{n-1} - 16a_{n-2}$ for $n \ge 2$ with initial conditions $a_0 = 16$ and $a_1 = 80$. Step 1: Write the characteristic equation as