Consider the relation R on Z? given by: R= {((a,b), (c, d)) : a + d = c+ b} Prove that R is an equivalence relation, and determine 3 elements of [(1,3)], the equivalence class of (1,3).

Q: Let R be a relation on A = {0, 2, 7, 8} and R = {(7, 2), (8, 8), (8,0), (2, 7), (2, 2), (7,0)}. Are…

A: The given relation R is defined on the set A = {0, 2, 7, 8}, and R = {(7, 2), (8, 8), (8, 0), (2,…

Q: Define a relation S on B={a,b,c,d} by S={(a,b),(a,c),(b,c),(d,d)}. Draw the directed graph of…

A:

Q: Given set A = {a, b, c, d} show the equivalence relation, which contains eight ordered pairs,…

A: Answer is in step 2

Q: Let A={1,2,3} and B={4,5,6). The set X={(1,4),(3,6),(2,4),(1,5)} is: O a relation between from A to…

A:

Q: The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is…

A: Option ATransitive.

Q: R is the equivalence relation on A = {1,2,3,4,5} defined below. how many subsets do the equivalence…

A: A binary relationship is a reflexive, symmetric, and transitive relationship of equivalence. The…

Q: Decompose R into a set of 3NF relations, that is lossless join and dependency preserving.

A: Here we decompose it in 3nf and check dependency preserving.…

Q: Consider the following set F of functional dependencies on the relation schema R = (A, B, C, D, E,…

A: a) Candidate Key : Minimal set of attributes used to differentiate every record of the table is…

Q: elp

A: help plz i will rate you  discrete structure

Q: Show that the order (Q, <q) has a least element but no greatest element, and it is a dense (in…

A: The question introduces a set equipped with a relation . The goal is to analyze the order structure…

Q: Normalization Here is a set of FDs for a relation R {A, B, C, D, E, F, G}; AB BC>DE AEF>G AC>DE a.…

A: Given, Relation schema = ( A, B, C, D, E, F, G ) The set of functional dependencies are : A -&gt; B…

Q: Suppose that we decompose the schema R = (A, B, C, D, E) into (A, B, C) (A, D, E). Show that this…

A: SOLUTION -   Given Relation R = (A,B,C,D,E) and dependencies are A --&gt; BC CD --&gt; E B--&gt;D…

Q: er the questions

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Q: Consider the relation R = {(a, d), (b, a), (b, c), (c, b), (c, c), (d, a)} on the set {a, b, c, d}.…

A: Below are the required answers :

Q: Define a relation R on Z×Z by (m,n)R(s,t) if and only if m-n = s-t. Is R reflexive? symmetric?…

A: In the given case, we prove all three one by one.

Q: "Observe that the values of h(n) seem to be related to powers of 3" In what way are 2, 5, 14, and…

A: h(n) = {1 if n = 1; 3 × h(n - 1) - 1 otherwise}We need to express this in polynomial/xponential…