...root of two. Example: If the universe of discourse is the set of all real numbers x where 0 ≤ x ≤ 1.0, then (x) x 2 ≤ 1.0 is true (x) x 2 ... ...se The English equivalents of these predicates are The square of any real number between zero and one inclusive is less than or equal to one. ... ... and one inclusive is less than or equal to one. 22 The square of any real number between zero and one inclusive is less than or equal to the nu... ...and one inclusive is less than or equal to the number. The square of any real number between zero and one is less than zero. The connectives of ... ... predicates. Example: If the universe of discourse is the set of all real numbers x where 0 ≤ x ≤ 1.0, then ((x) x 2 ≤ 1.0) /\ ((x) x 2 ≤ x... ...n { A, B } = B, then max { A, B } = A. iii) This proof is done using case analysis. Case 1: A ≥ B ≥ C B /\ C = C and then A \/ C = A, so the left... ...¬( A /\ B ) = ¬A \/ ¬B DeMorgan’s Proof: i) The proof is by case analysis Case 1: If A or B is one, then the left side is zero. One of t... ...n the right are one, so the conjunction is 1. iii) The proof is by case analysis Case 1: If one of the values is zero, then the conjunction in ... ...( A /\ B ) = ¬A \/ ¬B DeMorgan’s Proof: i) The proof is by case analysis. Case 1: A ≥ B Then A \/ B = A and the negation on the left is...