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Problem 7. Let the integers be our domain of discourse. Let p(x), q(x), r(x) be the propositional functions p(I) : I is odd r(r) : x is divisible by 3 (a) Write the following propositions in symbolic form (i) At least one integer is divisible by 3. (ii) No integer is equal to its square. (iii) If r is divisible by 3, then a is odd. (iv) All integers are divisible by 3. (b) For each of the statements from part (a), determine if the statement is true or false (You should have parts (i) through (iv) here). Justify each of your answers in the appropriate way (i.c. provide examples/counter examples when appropriate or provide a short explanation when appropriate)