MATH 301 – In Class Exercise 4 – Substitutabilty and Logical Implication

1. Let L = L_NT = {0, S, +, ×, E, <}. For each of the following formulas, , write out and then decide if t is substitutable for x in .

a) is and t is Sx.

b) is and t is Sy.

c) is and t is Sx.

2. Let L be any language. Let and be any L-formulas. Show that ╞.

You need to consider what is an abbreviation for, namely is short for .