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Midterm – in-class part
Time: 50 minutes (1) Decide if the following statement is true or false:
[a → (b ∨ c)] ∧ [b → ¬a] ∧ [d → ¬c] → [a → ¬d].
1
(2) How many integers between 1 and 800 inclusive are divisible by none of 4, 6, 8, 12, and 13?
(3) Use the principle of mathematical induction to show that 6|n3− n.
(4) If a = 17 and b = 29, find d = gcd(a, b) and the integers s, t such that d = sa + tb.
(5) Solve the following quadratic equation:
z2+ (1 + 4i)z − (5 + i) = 0.
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