+ Automatic Zoom 11) Suppose A={-4,-3,- 2,- 1,0,1,2,3,4} and R is defined on A by aRb...
Let R be the equivalence relation defined by aRb if a^2=b^2 (mod5) . Show that the relation is transitive. Also, determine the distinct equivalence classes.
QI. Let A-(-4-3-2-1,0,1,2,3,4]. R İs defined on A as follows: For all (m, n) E A, mRn㈠4](rn2_n2) Show that the relation R is an equivalence relation on the set A by drawing the graph of relation Find the distinct equivalence classes of R. Q2. Find examples of relations with the following properties a) Reflexive, but not symmetric and not transitive. b) Symmetric, but not reflexive and not transitive. c) Transitive, but not reflexive and not symmetric. d) Reflexive and symmetric,...
1. Define a relation on Z by aRb provided a -b a. Prove that this relation is an equivalence relation. b. Describe the equivalence classes. 2. Define a relation on Z by akb provided ab is even. Use counterexamples to show that the reflexive and transitive properties are not satisfied 3. Explain why the relation R on the set S-23,4 defined by R - 11.1),(22),3,3),4.4),2,3),(32),(2.4),(4,2)) is not an equivalence relation.
5. On the set of integers Z define the following relation: "aRb if and only if a - b is a multiple of 7." (1) Prove that R is an equivalence relation. 16 Marks] How many elements are there in the quotient set of 2 with respect to the equivalence relation R? Give reasons. |4 Marks
1. (2 marks) Let S 2,3,4,5,6,7,8,9, 10, 11, 12). Let r be the relation on the set S defined as follows: Va,bE S, arb if and only if every prime number that divides a is a factor of b and a S b. The relation T is a partial order relation (you do not need to prove this). Draw the Hasse diagram for T 1. (2 marks) Let S 2,3,4,5,6,7,8,9, 10, 11, 12). Let r be the relation on the...
From the proof of (ii) . Explain/Show why -n+ 1Sm-kn-1 is true by construction. . Explain/Show why 0 is the only number divisible by n in the range -n+1 ton-1 Proposition 6.24. Fix a modulus nEN. (i) is an equivalence relation on Z. (ii) The equivalence relation-has exactly n distinct equivalence classes, namely (ii) We need to prove that every integer falls into one of the equivalence classes [0], [1],..., [n -1], and that they are all distinct. For each...
1) Let R be the relation defined on N N as follows: (m, n)R(p, q) if and only if m - pis divisible by 3 and n - q is divisible by 5. For example, (2, 19)R(8,4). 1. Identify two elements of N X N which are related under R to (6, 45). II. Is R reflexive? Justify your answer. III. Is R symmetric? Justify your answer. IV. Is R transitive? Justify your answer. V.Is R an equivalence relation? Justify...
Let R be the relation defined on Z (integers): a R b iff a + b is even. Then the distinct equivalence classes are: Group of answer choices [1] = multiples of 3 [2] = multiples of 4 [0] = even integers and [1] = the odd integers all the integers None of the above
Question 11 Let's define an equivalence relation R on the set of integers by aRb if and only if 5|3a + 7b What is the cardinality of the partition induced by R? Not yet answered Points out of 1.00 P Flag question Select one: a. 1 O b.4 O C. 5 d. 2 O e. 7 O f. infinite
(14) Let R be a relation on the integers defined by m R n if and only if m+m2 n+ n2(mod 5). Show that R is an equivalence relation and determine all the equivalence classes.