4. Translate each of the following statements into a symboliclogic and tell if each of the following is true or false, with afull justification (you do not have to justify your answer to (ii),which was done before) : (i) Every integer has an additive inverse.(ii) If a and b are any integers such that b > 0, then thereexist integers q and r such that a = bq + r, where 0 ≤ r < b.(Note that this sentence does not have a uniqueness part of q orr.) (iii) Every integer has a unique multiplicative inverse.(Answer this question without using the symbol ∃! that we have notused much in class.) (iv) Any two real numbers x and y satisfy x< y. (v) Every real number has a greater real number. (vi) Thereexists a real number that is less than any real number. (vii) Thereare two real numbers x and y satisfy x < y. (viii) Given any tworeal numbers one of them is bigger than the other.
