CS 281 Solution to Test II
1 (a)
(b)
= =
=

2 (a)
(1)
(2)
(3) P
-------------


(b) (4) from (1) and Exportation
(5) from (3) and (4)
(6) from (2) and (5) with Hypothetical Syllogism.

3. Note that here we are trying to define for every natural number n.

Basis Clause: =
Inductive Clause: For every natural number n,
=
Extremal Clause:

4. Basis Step: Prove .

LHS = , and RHS = . Hence LHS = RHS.

Inductive Step: Prove if . .


=
=
= .

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