Computer Security: Art and Science

34.4 Exercises

1:
Prove that p (q r) = (p q) (p r)

using a truth table.
using natural deduction (show the rules that you apply at each step of the proof).
2:
Use the logical connectives of propositional logic to express the following sentences in propositional logic. Be sure to define all propositional atoms.

If the sun shines, we can make hay.
For dinner I can have a potato or rice but not both.
If you do all the homework, read the text, and study the lecture notes, then you will be prepared for the midterm exam. Otherwise, you may not be prepared for the exam.
3:
Use mathematical induction to prove that, for n 1,
4:
Use predicate logic to state the following sentences. Be sure to define all predicates, constants, and variables.

Not all birds can fly.
Every child is younger than its mother.
Mary and Sue have the same paternal grandfather.
5:
State which of the following strings are well-formed CTL formulas.

FGr
A¬Fp
¬ (¬p) (qr)
¬EXq
pU(AX)
AFq EXr

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1:	Prove that p (q r) = (p q) (p r) using a truth table. using natural deduction (show the rules that you apply at each step of the proof).
2:	Use the logical connectives of propositional logic to express the following sentences in propositional logic. Be sure to define all propositional atoms. If the sun shines, we can make hay. For dinner I can have a potato or rice but not both. If you do all the homework, read the text, and study the lecture notes, then you will be prepared for the midterm exam. Otherwise, you may not be prepared for the exam.
3:	Use mathematical induction to prove that, for n 1,
4:	Use predicate logic to state the following sentences. Be sure to define all predicates, constants, and variables. Not all birds can fly. Every child is younger than its mother. Mary and Sue have the same paternal grandfather.
5:	State which of the following strings are well-formed CTL formulas. FGr A¬Fp ¬ (¬p) (qr) ¬EXq pU(AX) AFq EXr