From the Text

Complete the following questions from the text:

• Section 2.2: 6, 16(b,d)
• Section 2.3: 6, 12, 13, 36(b), 37, 50.
  • Note the \(f(S)\) syntax was not mentioned in lecture, but is on p. 136 of the text.
  • The examples from the textbook's solutions will be worth zero.
• Section 2.4: 14, 32
  • For 32: For the countable sets, give a bijection between that set and one you know is countable (not necessarily the natural numbers). For the uncountable sets, give a bijection to a set you know is uncountable.

Questions

1. Prove or disprove that \(A\cap B \subseteq A\cup B\).
2. Is it possible that \(A\cap B = A\cup B\)? Give an example or prove that it is impossible.
3. Determine a formula for the value of \[\sum_{i=1}^{n} \left(x^{i}-x^{i-1}\right)\,.\]