Determine whether each relation is an equivalence relation. justify your answer. if the relation is an equivalence relation, then describe the partition defined by the equivalence classes.

(c) the domain is a group of people. person x is related to person y under relation s if x is currently the spouse of person y. you can assume that there is no polygamy and that there is at least one person who is married to another person in the group.

(d) the domain is the set of all integers. xey if x + y is even. an integer z is even if z = 2k for some integer k.



(a)

the domain of the equivalence relation d is the set s:

s = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17}

for any x, y ∈ s, xdy if x has the same remainder as y when divided by 4. show the partition of s defined by the equivalence classes of d.

Match the terms in the hlookup syntax with their explanation. a. lookup value b. data table c. row index d. mode 1. name of the table that contains the value 2. specifies if an exact match must be found 3. value to be searched 4. name of the row that contains the value

Given a link with a maximum transmission rate of 32.8 mbps. only two computers, x and y, wish to transmit starting at time t = 0 seconds. computer x sends filex (4 mib) and computer y sends filey (244 kib), both starting at time t = 0. statistical multiplexing is used, with details as follows packet payload size = 1000 bytes packet header size = 24 bytes (overhead) ignore processing and queueing delays assume partial packets (packets consisting of less than 1000 bytes of data) are padded so that they are the same size as full packets. assume continuous alternating-packet transmission. computer x gets the transmission medium first. at what time (t = ? ) would filey finish transmitting? give answer in milliseconds, without units, and round to one decimal places (e.g. for an answer of 0.013777 seconds you would enter "13.8" without the quotes)

Use a physical stopwatch to record the length of time it takes to run the program. calculate the difference obtained by calls to the method system.currenttimemillis() just before the start of the algorithm and just after the end of the algorithm. calculate the difference obtained by calls to the method system.currenttimemillis() at the start of the program and at the end of the program so that the elapsed time includes the display of the result. use the value returned by the method system.currenttimemillis() just after the end of the algorithm as the elapsed time.