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6. Let be a relation on Z defined as follows: a b if and only if 2a+36 is divisible by 5. (a) Show that is an equivalence relation. (b) What is the equivalence class of 0 ?

5. Define a relation R on the set of real numbers by (x, y) ER if and only if |1 – y <3. Is this relation reflexive? Is it symmetric? Is it transitive? Is this an equivalence relation? Justify your arguments.

Let T be a relation on R x R such that (a,b),(c,d) ∈ T if and only if a + b ≤ c + d.

a. Is T reflexive? If so, prove it. If not, prove that it is not.

b. Is T symmetric? If so, prove it. If not, prove that it is not.

c. Is T transitive? If so, prove it. If not, prove that it is not.

d. Is T an equivalence relation? If so, explain why it is. If not, explain why not.

e. Identify four numbers of [(-1, 2)]

SC Examining Distributions Checkp * + + C straighterline acrobatiq.com/en-us/courseware/summative-assessment/sl stats v1/v2_mi_checkpoint2 !! Apps M Gmail YouTube Maps Translate Here again are the boxplots showing annual incomes (in thousands of dollars) for households in two cities. Statstown Medianville- 140 0 20 40 60 80 100 120 Annual Income Which city has a greater percentage of households with annual incomes between $30,000 and 580,000? Statstown Medianville Both cities have the same percentage of households with annual incomes between $30,000 and $80,000 It is impossible to tell from the boxplots. Type here to search