SURNAME (BLOCK CAPITALS):
INITIALS:
STUDENT NUMBER:
SIGNATURE:
All questions concern our propositional logic and material covered in Chapter 3 of the course text. The marks for each question are shown in brackets.
Hence by TRANSITIVITY 3 times .
Hence by TRANSITIVITY 3 times, and EQUANIMITY we have that .
SOLUTION In state (p,q,r)=(T,T,F) the sentence evaluates to F. However is complete, and so the sentence cannot be a theorem.
SOLUTION Assume . However , and substitution with p:= P gives that . However , and so by Equanimity we have that . Metatheorem 3.7 states that any two theorems are equivalent, and in particular that . Leibniz with E being gives that , and so by equanimity, .