COS2661 ASSIGNMENT 2 SOLUTIONS 2021 SEMEMSTER 1 AND 2

COS2661 ASSIGNMENT 2 SOLUTIONS 2021 SEMEMSTER 1 AND 2

QUESTION 1 [15]
Write informal proofs for the following arguments, using proof by cases. Be as explicit as possible
about
each step in your proof.
a. Suppose you know that (Cube(a) Ù Small(b)) Ú (Cube(c) Ù Small(c)).
Show that Small(b) Ú Small(c) follows. (6)
Solution:
Using proof by cases either (Cube(a) Ù Small(b)) is true or (Cube(c) Ù Small(c)) is true. If
(Cube(a) Ù Small(b)) is true then Cube (a) is true and Small(b) is true. Since we know Small(c) is
true it means that Small(b) Ú Small(c) since at least one of them is true

If (Cube(c) Ù Small(c)) is true then it means small(c) is true, this in turn means Small(b) Ú Small(c)
is true since small (c) is true.

Small(b) Ú Small(c) is therefore true since in all the cases it remains true.

b) Suppose you know the following premises: (9)
1. Cube(a) Ú Tet(a) Ú Large(a)
2. ¬Cube(a) Ú a=b Ú Large(a)
3. ¬Large(a) Ú a=c
4. ¬(c=c Ù Tet(a))
Show that a=b Ú a=c follows.