Hello I need help with this ASAP

Proye the following statement by contradiction. If a and b are rational numbers, 1!) a! I], and ris an irrational number, then a + br is irrational. Proof by contradiction: Select an appropriate statement to start the proof. 0 Suppose not. That is, suppose there exist rational numbers a and b such that b at 0, r is a rational number, and a + Dr is irrational. 0 Suppose not. That is, suppose there exist irrational numbers a and b such that b s 0, r is a rational number, and a + br is rational. 0 Suppose not. That is, suppose there exist rational numbers a and b such that b at 0, r is an inational number, and a Dr is irrational. 0 Suppose not. That is, suppose there exist rational numbers a and b such that b a 0, r is an inational number, and a br is rational. 0 Suppose not. That is, suppose there exist irrational numbers a and b such that b at D, r is an irrational number, and a + Dr is rational. Then by definition of rational, ,3~=,b=i_,anda+br= d J n where c, cl, f, j, m, and n are | Select v | and | Select v . Since b a O, we also have that i # D. By substitution, +gz. d j :1 Solving this equation for r and representing the result as a single quotient in terms of C, d, L}, m, and :1 gives that Note that r a ratio of two integers because products and differences of integers integers. Also the denominator of r 0. Therefore, by denition of rational, it follows that r is , which contradicts the supposition. Hence the supposition is false and the given statement is true