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II.9 Exercises

Exercises [Slide 42]

Exercise 1.  

Why are the following not propositional formulae? There might be more than one reason

  • P¬Q
  • P Q
  • P¬ (Q )

Exercise 2.  

As seen in the course notes   false,f1 f2,f1 f2 and f1 f2 are derived propositional formulae.

Write out ((P Q) (Q P)) using only ¬and .

Exercise 3.  

Give the truth table for the following propositional formulae:

false
(¬P) (Q R)
(¬P) (Q ¬R)
(¬P) (Q R)

Exercise 4.  

Let σ0(P) = tt and σ0(Q) = tt.

Give the semantics of P Q, i.e., calculate MP Q(σ0).

Exercise 5.  

Show that for any state σ0 and for propositional variables P and Q the following holds MP Q(σ0) = (MP(σ0) or MQ(σ0)).

Exercise 6.  

Let P, Q, and R be propositional variables capturing the following propositions:

  • P: You get a first on the final exam
  • Q: You do every exercise of the course notes
  • R: You get a first for this module

Write the following as formulae using P, Q, and R and logical connectives.

  • You get a first for this module, but you do not do every exercise of the course notes.
  • To get a first for this module, it is necessary for you to get a first on the final exam.
  • Getting a first on the final exam and doing every exercise in the course notes is sufficient for getting a first in the module.

Exercise 7.  

Determine which of the following formula is satisfiable or valid. Explain why.

  • false
  • false true
  • (P Q) ≡¬(¬P ¬Q)
  • (P (P Q)) P







2018-03-10
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