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Notes: Assignment #1 Please refer to Homework & How to turn-in your assignments sections of "Course_Outline_Details" file for details regarding groupwork, how to turn in your assignments. Q1: Determine whether the following statements are true or false. Provide reasoning as well. (a) If X₁ ≤ X2 and X2 X3, then X₁ ≤ X3. Tru (b) Continue from part (a). What is the necessary condition that you need to be able to state that X₁ = X2 = X3? (c) Let X3 = X₁ UX₂ and X₁ = X₁ NX2. If X₁ = X2, then X4 C X3. Q2: Consider the following infinite series. 8 ∞ Σh(n) = f(n) Σ n=0 n=0 (a) If the series converges, what can you say about the relationship between f(n) and g(n)? (b) If the series diverges, what can you say about the relationship between ƒ (n) and g(n)? Hint: You may specify the functions: f(n) = x^and g(k) = xk. What is the relationship between n and k? Q3: In general, fogg of. Provide an example of such f(x) and g(x). Bonus Q: ex = 00 .n x n=0 x x² x3 2! 3! = 1+ + + + n! 1! Using the fact that ex and ln(x) are inverses of each other, explain why ln(0) is undefined. Hint: First, start off by looking at first few terms of ex. That is, see if ex > 0Vx ≥ 0. Then, do the same thing for x < 0. You should be able to determine the range for ex Vx = R at this point. Now, what are the domain and range of In(x)?