True or false if the statement is not true give a counterexample.
1.If a>b,and c is positive, then ac>bc?
2.if a^2=b^2,then a=b?
3. If a>b,and c is positive,then a/c>b/c?
T
F (-2)^2 = 2^2
T
1. The statement is true. To prove it, we can use the properties of inequalities. Given that a > b, we can multiply both sides of the inequality by a positive number (in this case, c) without changing the inequality sign. Therefore, ac > bc.
2. The statement is false. A counterexample would be a = -2 and b = 2. In this case, (-2)^2 = 2^2, but -2 ≠ 2.
3. The statement is true. Again, we can use the properties of inequalities. Given that a > b and c is positive, we can divide both sides of the inequality by a positive number (in this case, c) without changing the inequality sign. Therefore, a/c > b/c.