Problem 1:

A. Rewrite the following sentences using mathematical symbols (you do not need to write them as implications):

i) All integers greater than 3 are either prime or even.

ii) There exists some x between 5 and 10 with 12(x)2being a multiple of 3.

iii) All even numbers can be written as a sum of two prime numbers.

iv) The product of any two integers is also an integer.

B. Using p,q, r and s to represent basic mathematical statements, use the connecting symbols for compound statements and negations to express the structure of the given statements (please use consistent letter for each statement throughout the exercises):

i) If I make the bed this morning and I do the dishes, then I will have a clean apartment

ii) If you don't have a clean apartment or you don't do the dishes, then you have to order food for dinner.

iii) I make the bed whenever I have a clean apartment.