Answer Happy

Question 1:
Write the truth table for the proposition ¬(r∧¬q) → (p∨¬r). Show
all intermediate columns. Is the proposition a tautology?
Question 2:
Show that the conditional statement in (¬q∧(p∨q)) → p is a
tautology without using truth tables. Use only one(!) logical
equivalence in each step and refer to it.
Question 3:
We have the following statements::
• I(x) the person x has passed an entrance exam.
• M(x) the person x studies at a music school.
• L(x,y) the person x has completed the course y.
Write the statements using these predicates, any needed
quantifiers as well as I(x), M(x) and L(x,y).
a) Anna studies at a music school but Finnur does not study at a
music school.
b) Everyone who studies at a music school has passed an entrance
exam.
c) Express each of these by an English sentence:
– ∀x∃y(L(x, y))
– ∃y∀x(¬L(x, y))")
p192