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Logic and Proof

Logic and Proof

Logic and Proof: Make a (Mathematical) Statement True or False

1. Is the statement "1 + 1 = 2 or any two points determine a line" true or false? -> False
2. What is the converse of rz? -> zr
3. Which of "and," "not," and "or" link two statements together? -> "not"
4. How many values of x make the statement "x ≤ 5 and x ≥ 5" true? -> Infinitely many
5. Suppose we know ab, bc. If we know b is true, may we infer c? -> Yes, by detachment
6. Is the contrapositive of "Everything brown is a dog" true? -> No, and a white dog is a counterexample
7. Which is an example of something "white or not soft?" -> White rock candy
8. Suppose that pq and pr. May we infer that qr? -> No
9. What is the converse of not p → not q? -> not q → not p
10. The statements pq and qr are given. If we know q to be true, which of the following CANNOT be assumed as true? -> p