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