Let A = {1,2,3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2, 3R5 and 6R3. Also assume R has 3 equivalence classes, no equivalence class has 4 members, and [4] has only one member. Determine the equivalence classes of R. (Hint: it may help to draw the digraph representation of R.)
Let A = {1,2,3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2, 3R5 and 6R3. Also assume R has 3 equivalence classes, no equivalence class has 4 members, and [4] has only one member. Determine the equivalence classes of R. (Hint: it may help to draw the digraph representation of R.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let A = {1,2,3, 4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2,
3R5 and 6R3. Also assume R has 3 equivalence classes, no equivalence class has 4 members, and
[4] has only one member. Determine the equivalence classes of R. (Hint: it may help to draw the
digraph representation of R.)
Define a relation S CR x R by S = { (x, y) E R × R |x – y E Z }. Prove that S is an
equivalence relation on R.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b20ac81-2c30-4a90-b93e-f9efe665359b%2F595802f2-b8f9-4fc7-a4d3-d072dcfe8a2b%2Fxvf8xbt_processed.png&w=3840&q=75)
Transcribed Image Text:Let A = {1,2,3, 4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2,
3R5 and 6R3. Also assume R has 3 equivalence classes, no equivalence class has 4 members, and
[4] has only one member. Determine the equivalence classes of R. (Hint: it may help to draw the
digraph representation of R.)
Define a relation S CR x R by S = { (x, y) E R × R |x – y E Z }. Prove that S is an
equivalence relation on R.
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