3. Convert the following either to English sentences, if written using propositional logic, or to propositional logic, if written in English. Try to avoid using English phrases, like "if" and "then" in your formal logic, and instead rely on symbols, like . (a) [5 points] If the square of an integer is greater than 9 , then that integer is greater than 3 or it is less than 3. CSCI 1311 Discrete Structures I PS 2 (b) [5 points] For every integer, there exists an integer that is less than that integer. (c) [5 points] Every real number is a complex number. (d) [5 points] (x,yZ)(x>1y>1)[(zZ)(x3+y3=z3)] (e) [5 points] (x,yR)(x1(p,qZ)(p+q=2xPrime(p)Prime(q))] 4. Which of the following assertions are true or false for the proposition P(x,y). For any false assertion, provide a counterexample statement for which the assertion is false. For any true example, provide a brief explanation for why it is true. (a) [4 points] xyP(x,y)yxP(x,y) (b) [4 points] xyP(x,y)yxP(x,y) (c) [4 points] xyP(x,y)yxP(x,y) (d) [4 points] xyP(x,y)yxP(x,y) (e) [4 points] xyP(x,y)yxP(x,y)