Exercise Chapter 2.6

1. b:- a.

   Note that b is true if a is true.

2. c:- a.
   c:- b.

   Here we have a straight use of disjunction.

3. c:- a, b.

   Here is a straightforward example of a conjunction.

4. d:- a, b.
   d:- a, c.

   This is a hard one. We cannot (yet) write what we want to write: that is, d:- a, (b or c). Here, we can use de Morgan's law: this is the equivalence: a (b c) d (a b) (a c) d.

5. b:- a.

   This is hard too. The obvious solution is:
   

   not a.
   b.

   but this is not allowed. Consequently, we have to transform the expression using the logical equivalence a b b a.