In (a) - (c), determine whether the given relation is an equivalence relation. I
ID: 2962835 • Letter: I
Question
In (a) - (c), determine whether the given relation is an equivalence relation. If the answer is yes, find the equivalence classes. Explain in detail
a) A = { 1, 2, 3}, R= {( 1,1), (2,2), (1,2) (2,3)}
b) A { 1,2,3}, R= (1,1), (2,2), (3,3), (1,3), (3,2)}
c) A= the set of all integers and define m R n if and only if m and n have the same remainder when divided by 4
In the following exercises, compute the given arithmetic expression and write the answer in the form a + bi for a, b in R.
a) (5+3i) (4- 2i)
b) | 4- 3i|
c) (6 + 4i)- (7- 5i)
d) 2-3i/ 5+4i
find all solutions for the following equation z^3= -1
compute AB if
A= -1 1 2 B= 1 2
0 1 3 0 3
1 5
Explanation / Answer
(a)not a equivalence relation
since (1,2), (2,3) belongs to R but not (1,3)
(b)not a equicalence relation
since (1,3),(3,2) belongs to R but not (1,2)
(c)equaivalence relation
equivalence class: [0], [1],[2],[3] each representing remiander when divided by
(a)(5+3i) (4- 2i) = 20 +12i-10i +6 =26+2i
(b)((-3)^2 +4^2)^0.5 = 5
(c)(6 + 4i)- (7- 5i) = 6-7 +(4-5)i = -1-i
(d)2-3i/ 5+4i = (2-3i)(5-4i)/(5+4i)(5-4i) = (10 -15i-8i -12)/(25+16) = (-2-23i)/41
(e)-1, 1/2 +sqrt(3) *i/2, 1/2 -sqrt(3) *i/2
AB =
[1 11
3 18]