Relations a) suppose m, a, be z and m > 0. prove that the following relation satisfy the properties of equivalence relation. (10pts) divides (a - b) m1(a-b) i. e. m
b) consider the following relations on the set of integers: r1: (r, y)l y} r2: (x, y)l> y} r3: {(x, y)l= y c r4: (r, y)z= y} r5: {(x, y)lz= y + 1} r6: {(r, y)|+y

Design an er diagram for keeping track of information about votes taken in the u.s. house of representatives during the current two-year congressional session. the database needs to keep track of each u.s. state's name (e.g., texas', new york', california') and include the region of the state (whose domain is {northeast', midwest', southeast', southwest', west'}). each congress person in the house of representatives is described by his or her name, plus the district represented, the start date when the congressperson was first elected, and the political party to which he or she belongs (whose domain is {republican', democrat', 'independent', other'}). the database keeps track of each bill (i.e., proposed law), including the bill name, the date of vote on the bill, whether the bill passed or failed (whose domain is {yes', no'}), and the sponsor (the congressperson(s) who sponsored - that is, proposed - the bill). the database also keeps track of how each congressperson voted on each bill (domain of vote attribute is {yes', no', abstain', absent'}). additional information: