MATH 301 – In Class Exercise

1. Let L = {a, b, f, r} be a language with a and b constants, f a binary function and r a binary relation.

a) Write out all the terms that are contained in the term i. ffabv and in the formula ii. rafafbb.

b) Assuming that you can use only one variable, x, write out 12 different terms in the language L.

c) Write a formula with five symbols.

d) Write a formula with seven symbols.

e) Write a formula with eight symbols.

2. Let L = { +, ×} be a language with two binary functions thought of as addition and multiplication. Write out the formula that expresses the distributive law of multiplication over addition without using parentheses.

3. Let L = {a, b, f, g} be a language with a and b constants and f and g binary functions. Show that (Ø=fgabfbbgafbb) is a formula by breaking it down into terms and applying the definition of a formula. Is it atomic?