Question

Got part a and b, but I can't figure out part c.

a) In general, the claim is false. Demonstrate a counterexample. b) For some real numbers, the claim is true. Demonstrate two examples, one positive and one negative. C) Suppose the claim is true for a particular ye R. What can you say for certain about the real number y? In other words, what are some necessary conditions for the claim to be true?

Answer 1

Given the following data claim v times elementof R [3x] - 3[x] + 1 and [2x] = 2[x] a take, x = 1 implies [x] = 1, 3x = 3 implies [3x] = 3 = 3 = 4 take b take, x = 1.6 [x] = 1, [x] = 2 = 3x = 4.8 rightarrow [3x] = 4, 2x = 3.2 implies [2x] = 4 (3x) = 4 = 3 times 1 + 1 = 3[x] + 1 And [2x] = 4 = 2 times 2 = 2[x] take, x = -5.4 implies [x] = -6, [x] = -5 = 2x = -10.8 implies [2x] = -10, 3x = -16.2 implies [3x] = -17 = 3x(- 6) + 1 implies [3x] = 3[x] + 1 - 10 = 2x(- 5) implies [2x] = 2x[x] c y notequalsto integer, y = I + f rightarrow traditional pore rightarrow part from the claim to be true