[Solved] MATH221 Mathematics for Computer Science Assignment Two

Question 1. [4 Marks]

• Find a natural number n such that 2 1066 + 1492 n (mod 1776). Is n unique?
• Show that there is no n N such that n 3 (mod 4) and n 5 (mod 8).

Question 2. [4 Marks] Identify the shaded regions, using only the union, intersection and complement symbols.

Question 3. [4 Marks] What is the coefficient of x⁵ in the expression (4 + 3x)¹²? (Do NOT multiply 4 + 3x by itself 12 times.)

Question 4. [8 Marks] Prove or disprove that the following are equivalence relations. If you find one (or both) that is an equivalence relation, write out [1] and .

• For a,b,c,d Z with
• For x,y R: R = {(x,y) : |x y| 1}.