2. Draw an expression tree for the following algebraic expression with the symbol-in the root of the tree (do not simplify the expression) The truly correct expression is: (x + y) ((z . (y +5)1+ ((z + i)-y)) Treat and as node contents, just like r and y 3. In each case below, either draw a graph with the required properties, or prove that it doesn't exist (based on the results of Lecture/Workshop 9) (a) A connected graph without loops or multiple edges and with 5 vertices whose degrees are 1; 1; 2; 3: 4 (b) A connected graph without loops or multiple edges and with 5 (c) A tree with 8 vertices whose degrees are 1; 1;1 1: 1; 4;4 tion (no check is required) S(n)--3S(n-1) 2S(n-2) S(0) 1, (1)-3, (where n22) vertices whose degrees are 1; 2; 2; 2; 3. 4. Give a complete solution, for the second order order recurrence rela- You must include al the relevant words in your solution such as; Standard Form, "Homogeneous", "Characteristic Equation" "Gen eral Solution" and others. You can use abbreviations like. Char. eq. . Gen. Sol 5. Consider the first order recurrence relation: (a) Calculate T2, Ts and T4 using iteration. Give detailed answers. (b) Give a complete solution, including the check, for the recurrence relation above. You must include all the relevant words in your solution such as; "Standard Form, Homogeneous", "Characteristic Equation". General Solution and others. You can use abbreviations like . Char. eq. Gen. Sol