Problem 1 There are two parts: [Lecture Slides 10, page 18]:

(a) Prove one side of the equivalence in the exercise in [Lecture Slides 13, page 32], specifically

Þ→ V (not V Þ), after replacing and ; by propositional variables p and q₁, for i = 1, 2, 3.

(b) Prove one side of the equivalence in the exercise in [Lecture Slides 13, page 33], specifically

Þ→ V (not $), after replacing , and ; by propositional variables p; and qi, for i = 1, 2, 3,

but leave as a generic (i.e., unknown) wff with two free variables.

In both parts, we ask you to choose a proof-theoretic, not semantic, approach. Proof-theoretically,

you can choose natural deduction or also tableaux, even though in the case of tableaux we have not yet

mentioned expansion rules for quantifiers in lecture (but these are easy to formulate - left to you!). O