1. The problem statement, all variables and given/known data Here are a few questions from an exercise sheet that I need help on. I really don't have a clue on how to start them. Could anyone help me attempt at each a) for each question? 1. Use (nested) quantifiers (∀ and ∃) (and propositional junctors) and only equality ``='', conventional ordering ``≤'', ``<'', etc., and divisibility ``|'' as predicates, and arithmetic operators as functions to express the following statements as predicate logic formulae: a)**“Exponentiation on reals distributes over multiplication to the left.” b)**“Each positive real number has a logarithm.” c)**“Exponentiation on reals has no left identity.” d)**“Any two natural numbers have a least common multiple.” e)**“There are infinitely many primes. (I.e., for each natural number, there is a prime number above it.)” f)**“Each Pythagorean triple involves at least one even number.” 2. Assume that Q and R are relations on a set A. Prove (using relation-algebraic calculations) or disprove (by providing counterexamples) each of the following statements. a)**If Q and R are both reflexive, then Q ∩ R is reflexive, too. b)**If Q and R are both reflexive, then Q ∪ R is reflexive, too. c)**If Q and R are both transitive, then Q ; R is transitive, too. d)**If Q and R are both symmetric, then Q ∩ R is symmetric, too. e)**If Q and R are both transitive, then Q ∪ R is transitive, too. f)**If Q is symmetric, then Q ; Q is symmetric, too. 3. The attempt at a solution 1a) ∀x∀y∀z((xy)z = xzyz | x,y,z ∈ ℝ) 2a) not sure how to start... Many thanks.