# CS245 Lecture Notes - Lecture 1: University Of Waterloo, Parallelogram, Quadrilateral

UNIVERSITY OF WATERLOO

Computer Science 245, Winter 2016

Applied Logic for Computer Science

ASSIGNMENT 1

Given: Monday, January 11, Due: Tuesday. January 19, 4:30pm

Problem (1)

1. R∧ ¬O(R: “Jane loves rock-and-roll”; O: “Jane likes opera”)

2. J∨E(J: “Jerry will get to the top of the mountain”; E: “Elaine will get

to the top of the mountain”)

3. ¬S(S: “All sailors are good swimmers”)

4. (O∨G)∧¬(O∧G) (O: “Oscar dates Virginia”; G: “George dates Virginia”)

5. ¬(H∧S)→ ¬P(P: “Oscar will pass the logic course”; H: “Oscar does

his homework”; S: “Oscar studies”)

6. D→(O∧V→S) (D: “Logic is diﬃcult”; O: “Oscar will pass”; V:

“Virginia will pass”; S: “Oscar and Virginia study”)

7. Q→(P↔E∧L) (Q: “Qis a quadrilateral”; P: “Qis a parallelogram”;

E: “Opposite sides of Qare equal”; L: “Opposite sides of Qare parallel”)

8. P→ ¬I∧ ¬C(P: “The two lines in question are parallel”; I: “The two

lines in question intersect”; C: “the two lines in question coincide”)

9. D→(I→P) (D: “The derivative of fis deﬁned on the interval (a, b)”;

I: “fis increasing”; P: “The derivative of fis positive on the interval

(a, b)”)

10. C∧A∧B→M(M: “fhas a maximum on the interval [a, b]”; A: “fis

continuous at a”; B: “fis continuous at b”; C: “fis continuous on the

interval (a, b)”)

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