ex1_ans - COMP1002 Theory 1 Exercises I: Basic...

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COMP1002 Theory 1 Exercises I: Basic propositional logic. With answers. Robin Hirsch November 26, 2010 Here is the definition of a propositional formula: proposition::= p | q | r | p 0 | p 1 | p 2 | ... bin connective::= ∧| ∨ | → | ↔ formula ::= proposition formula | (formula bin connective formula) Which of the following are propositional formulas? You should use the definition above quite rigidly to determine your answer. 1. p Answer: yes 2. ( p q ) Answer: yes 3. ( p q r ) Answer: no — could write (( p q ) r ) instead though 4. ¬ ( p ) Answer: no — cannot put brackets round p 5. ( p ( q p )) Answer: yes 6. p q Answer: no — brackets needed 7. ( p q ) ( p ∨ ¬ q ) Answer: no — missing outer brackets Translate the following English sentences into propositional logic, clearly identifying your el- ementary clauses. Answer: Let n = “I will go”, p = “you will go”, q = “It will rain soon”, r = “Crop will fail”, s = “I drink too much”, t = “I pass out”, u = “I do something outrageous”,
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This note was uploaded on 05/12/2011 for the course CS 430 taught by Professor Latifa during the Spring '11 term at Occidental.

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ex1_ans - COMP1002 Theory 1 Exercises I: Basic...

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