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1. Consider the following statement: "For every natural
number n, there exists a prime number p such that p > n". Is
this statement true or false? Explain your reasoning.
 - A) True, because there are infinitely many prime
numbers.
 - B) False, because there are only finitely many prime
numbers.
 - C) True, because of Euclid's theorem.
 - D) False, because of the prime number theorem.
 - Answer: C) True, because of Euclid's theorem. Euclid's
theorem states that for any natural number n, there is a
prime number p greater than n. This can be proved by
considering the product of the first n primes plus one,
which is not divisible by any of the first n primes, and
therefore must have a prime factor greater than n.
2. Let A = {1, 2, 3, 4} and B = {2, 4, 6, 8}. What is the
cardinality of A ∪ B? Show your work.
 - A) 4
 - B) 5
 - C) 6
 - D) 8
 - Answer: C) 6. The cardinality of a set is the number of
elements in the set. To find the cardinality of A ∪ B, we
need to count the number of elements that are in either A or
B or both. We can use the formula A ∪ B = A + B - A
∩ B , where A ∩ B is the cardinality of the intersection of
A and B. In this case, A = 4, B = 4, and A ∩ B = 2,
since A and B have two elements in common: 2 and 4.
Therefore, A ∪ B = 4 + 4 - 2 = 6.
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