Question 1. Are the following statements true or false? Justify your answer. 1. If the moon is larger than the earth then the ea
rth is larger than the sun. 2. The moon is larger than the earth if and only if ∃x (2x = 5) (given that the domain of x is the set of all integers). Question 2. 1. How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 = 100, where x1, x2, x3, x4, x5 are nonnegative integers. 2. Let a be a real number other than 1. By the mathematical induction, prove that 1 +a+a 2 +· · ·+a n = (a n+1 − 1)/(a − 1) for all n ≥ 1.
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