This is actually 2-3 time uploading it.

I want formal proof. thanks.

1. [10 marks] Difference of Squares. Let n +, we say that n is a difference of squares if it is of the form p2 - for some positive integers p and q. We can capture this definition in the following predicate, defined over Z+ DifferenceOfSquares(n): 3p, q EZ+ , n-p2-q2 (a) Translate the following statement into predicate logic: "Every difference of squares is odd or divisible by four." You may use the DifferenceOfSquares predicate in your translation, but you must expand the defi nition of divisibility (including in how you express "odd") (b) Prove the statement from part (a). Use the definition of divisibility; do not use any external facts about divisibility, except that you may use the Quotient-Remainder Theorem1 to identify cases for your proof (c) (Corrected Jan 31)2 Prove or disprove the following statement Vr,yEZt, DifferenceOfSquares() A DifferenceOfSquares()DifferenceOfSquares( y) If you want to disprove this statement, first write the negation of the statement in predicate logic You may, but are not required to, use part (a) in your proof/disproof