Exercise 2.5.4: Proof by contrapositive of algebraic statements. About Prove each statement by contrapositive (a) For every pair of real numbers and , if , then . Solution (b) For every pair of real numbers and , if , then or . (c) For every pair of positive real numbers and , if , then or .

The table shows the relationship between the number of cups of cereal and the number of cups of raisins in a cereal bar recipe: number of cups of cereal number of cups of raisins 8 2 12 3 16 4 molly plotted an equivalent ratio as shown on the grid below: a graph is shown. the title of the graph is cereal bars. the horizontal axis label is cereal in cups. the x-axis values are 0, 20, 40, 60, 80,100. the vertical axis label is raisins in cups. the y-axis values are 0, 10, 20, 30, 40, 50. a point is plotted on the ordered pair 40,20. which of these explains why the point molly plotted is incorrect? (a) if the number of cups of cereal is 40, then the number of cups of raisins will be10. (b)if the number of cups of raisins is 40, then the number of cups of cereal will be10. (c) if the number of cups of cereal is 40, then the number of cups of raisins will be 80. (d) if the number of cups of raisins is 40, then the number of cups of cereal will be 80.