Final Exam (d) B∧ ∼ B (e) A∧ ∼ A 8. The denial of the statement “All red boats sail on blue water” is (a) (b) (c) (d) (e)
Some red boats sail on blue water. There is some red boat that sails on water that is not blue. All red boats do not sail. Some red boats do sail. This red boat is for sale.
9. The method of proof by contradiction is useful for (a) (b) (c) (d) (e)
Proving that something is false. Proving that something is undecidable. Proving that something is true. Proving that something cannot be proved. Disproving something.
10. The method of mathematical induction involves (a) (b) (c) (d) (e)
Infinitely many steps. A contradictory step. A bootstrap step. An important inductive step. An indeterminate step.
11. The method of direct proof is important because (a) (b) (c) (d) (e)
It is indirect. It is valid. It is invalid. It applies to most proofs. It is logically simple.
12. If A = {1, 2, 3} and B = {2, 3, 4} then (a) A ⊂ B (b) B ⊂ A (c) A ∩ B = ∅
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