With a binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to b, how many tuples need to be added to the relation Rbelow in order to make it symmetric R={ (0,2), (0, 3), (0, 4), (1, 1), (1, 3), (2, 0), (2, 1), (2, 2), (3,0), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2) } where A = {0, 1,2, 3, 4} Select one: O 3 O 4 O none of these options O 5 O 6

How many relations are there on the set {a, b}. Show all possible relations on the set {a, b} in matrix format.

6. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation xRy when x + y is divisible by 3, then R = O {1, 2), (2, 4)} all of these O {(1, 2), (2, 4), (3, 3)} O {1, 2), (3, 3)}

For the binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to b, which of the following statements would be true? R={ (0,4), (1, 1), (1, 3), (1, 4), (2, 1), (2, 2), (3, 2), (4, 4) } where A = {0, 1,2, 3, 4} Select one: O Ris symmetric but not antisymmetric O Ris antisymmetric but not symmetric O Ris both symmetric and antisymmetric O none of these options O Ris neither symmetric nor antisymmetric

Suppose R and S are relations on {a, b, c, d}, where R = {(a, b), (a, d), (b, c), (c, c), (d, a)} and S = {(a, c), (b, d), (d, a)}. Find R• S.

How many relations are there on the set {a, b, c, d}

The R is the relation from {1, 2, 3} to {1, 2, 3, 4} with R = {(1, 1), (1, 2), (2, 3),(3, 4), (3, 4)} and S is the relation from {1, 2, 3, 4} to {0, 1, 2} with S = {(1, 0),(2, 1), (3, 2), (3, 0), (4, 1)}. Find the composites of the relations SoR and RoS.

PLEASE TYPE ONLY*** In  a scout camp each girl is familiar with exactly 10 boys and each boy is familiar with exactly 10 girls.If the familiarity relation is symmetric, prove that the number of girls and the number of boysin the scout camp are equal.

1. Let A = {1,2,3,4,5,6}, and consider the following equivalence relation on A: ! = {(1,1), (2, 2), (3, 3), (4, 4), (5,5), (6,6), (2, 3), (3,2), (4, 5), (5, 4), (4, 6), (6,4), (5, 6), (6,5)}. R = List the equivalence classes of R. 2. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose R has two equivalence classes. Also aRd, bRc and eRd. Write out R as a set. 3. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose R has three equivalence classes. Also aRd and bRc. Write out R as a set. 4. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose also that aRd and bRc, eRa and cRe. How many equivalence classes does R have? 5. There are two different equivalence relations on the set A = {a, b}. Describe them. Diagrams will suffice. 6. There are five different equivalence relations on the set A = {a,b,c}. Describe them all. Diagrams will suffice. 7. Define a relation R on Z as xRy if and only if 3x-5y is even. Prove R is an equivalence…

Let ? = {1, 2, 3, 4, 5, 6, 7} and define a relation ? ⊆ ? × ? by? = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6), (5,5)}Determine (yes or no) whether ? has the following properties (no justification is required).