Name: diane Who is asking: Student Level of the question: Secondary Question: I What is the largest real number less than 10? 1- there is no largest real number less than 10 or 2- 9 or 3- 9.999... II Given that not (a and b) implies c.What does (not c) imply ? 1-a and b 2- (not a and b) or (a and not b) 3- (not a and b) or (a and not b) 4- a or b III What are the x and y intercepts of the equation 2x + 3y -6 =0 ? 1- x=3 and y=2 2- x=6 and y=-2 3- -3x + 2y =0 I hope you can help me Thank-you, Hi Diane, I 9.1 is a real number less than 10 and graeter than 9, so can't be #2 9.999... (if this is the infinite repeating decimal) Let x = 9.999.... Then 10x = 99.999... So 9x = 10x - x = 99.999... - 9.999... = 90 Thus, x = 90/9 = 10 Therefore, can't be #3. Hence, by a process of elimination, the answer is #1. (note: this answer also makes sense because, for any real number less than 10, we can always find a larger real number less than 10 - the real numbers are infinitely dense) II a and b means both a and b are true so not (a and b) means either a is false and b is true (*), or a is true and b is false (**), or a is false and b is false (***). Thus, not c implies not [not (a and b)], which means (*) and (**) and (***) are false. In other words, a is true and b is true. Therefore, not c means a and b. Hence, the answer is #1 Another way to see this: "not" undoes "not" That is, not (not p) = p for any proposition p Therefore, not c = not [not (a and b)] = a and b. III x intercept: set y = 0 2x + 3(0) - 6 = 0 2x = 6 x = 3 y intercept: set x = 0 2(0) + 3y - 6 = 0 3y = 6 y = 2 Therefore, the answer is #1. Paul