Question

3. (10+8) Consider the relation, R, on the set A = \{-2, -4, -1, 0, 3, 6, 9\}. For x, y ? A, xRy if x - y = 5m for some integer m. (A) Verify that this relation is transitive. You can't use the condition in (B). (B) It is well known that R is an equivalence relation. No need to verify. Find two of its equivalence classes.

          3. (10+8) Consider the relation, R, on the set A = \{-2, -4, -1, 0, 3, 6, 9\}.
For x, y ? A, xRy if x - y = 5m for some integer m.
(A) Verify that this relation is transitive. You can't use the condition in (B).
(B) It is well known that R is an equivalence relation. No need to verify. Find two of its
equivalence classes.

3. (10+8) Consider the relation, R, on the set A = {-2, -4, -1, 0, 3, 6, 9}.
For x, y ? A, xRy if x - y = 5m for some integer m.
(A) Verify that this relation is transitive. You can't use the condition in (B).
(B) It is well known that R is an equivalence relation. No need to verify. Find two of its
equivalence classes.

Added by Adri-N M.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Sri K

02/12/2023

Step 1

To verify that the relation R is transitive, we need to show that if xRy and yRz, then xRz for all x, y, and z in A. Let's consider three elements x, y, and z in A such that xRy and yRz. If xRy, then x - y = 5m for some integer m. If yRz, then y - z = 5n for Show more…

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3. (1o+8) Consider the relation, R, on the set A = {-2, --4, -1,0,3,6,9} For x,y e A, xRy if x - y = 5m for some integer m. (A) Verify that this relation is transitive. You can't use the condition in (B) (B) It is well known that R is an equivalence relation. No need to verify. Find two of its equivalence classes.