1. The problem statement, all variables and given/known data Given a series of mathematical statements, some of which are true and some of which are false. Prove those of which are true, and disprove those which are false. 1. The sum of three odd integers is odd. Text: Principles of Mathematics by Allendoefer and Oakley. 2. Relevant equations ∀x(px→qx)↔P⊆Q Law of Detachment and Law of Substitution. 3. The attempt at a solution I am mainly looking for feedback on my notation (formalism). What is the proper way of writing out a proper basic proof? Statement: The sum of three odd integers is odd. ∀x(integers): If x is odd, then ∑3i=1xi is odd. (1) Assume x1, x2, and x3 is odd. [Hypothesis] (2) The integers a, b, and c exist such that x1=2a+1, x2=2b+1, and x3=2c+1. [Defn of odd] (3) ∑3i=1xi =(2a+1)+(2b+1)+(2c+1) =2a+1+2b+1+2c+1 =2a+2b+2c+2+1 =2(a+b+c+1)+1 =2(m)+1[Let m=a+b+c+1] Therefore the sum of three odd integers is odd by definition.