Please solve all questions.

CPS 341 HOMEWORK 3. Due at class time, in class, Thursday, 15 February, 2018 Partial credit is possible only if you do your work in steps You must prove using the method specified. You must write clearly and in complete sentences. Make sure you read the hidden quantifiers in the sentences so that you can interpret the structure of the sentences correctly. (1) The domain is integers (1a) (4 pts) Write the following using logical connectives, quantifiers, and required mathematical symbols The difference of squares of two odd integers is a multiple of 4 (1b) (8 pts) Write a direct proof of the proposition in (la) (2) The domain is integers (2a) (4 pts) Write the following using logical connectives, quantifiers, and required mathematical symbols If the sum of the squares of two integers is even then either both the integers are even or both the integers are odd (2b) (8 pts) Prove the proposition in (2a) by contraposition (3) (6 pts) The domain is integers. Consider the following proposition For every positive integer n,