Show that the relation S in the set A={x...

Show that the relation `S` in the set `A={x\ \ Z\ :0\ lt=x\ lt=12}` given by `S={(a , b):\ a ,\ b\ \ Z ,\ \ |a-b|` is divisible by `4}` is an equivalence relation. Find the set of all elements related to 1.

Topper's Solved these Questions

CUET MOCK TEST 2022
XII BOARDS PREVIOUS YEAR|Exercise Question|49 Videos

Similar Questions

Explore conceptually related problems

Show that each of the relation R in the set A={x in Z:0<=x<=12} given by (i) R={(a,b):|a-b| is a multiple of 4} (ii) quad R={(a,b):a=b} is an equivalence relation.Find the set of all elements related to 1 in each case.

Show that the relation R on the set A={x in Z:0<=x<=12}, given by R={(a,b):|a-b| is a multiple of 4} is an equivalence relation.Find the set of all elements related to 1 i.e.equivalence class [1]

Let R={(a,b):a,b in Z and (a-b) is divisible by 5}. Show that R is an equivalence relation on Z.

Show that the relation S on the set : A={x inZ:0lexle12} given by: S = { (a,b):a,binZ,|a-b| is divisible by 3} is an equivalence relation.

Let R be the relation on set A={x:x in Z, 0 le x le 10} given by R={(a,b):(a-b) "is divisible by " 4} . Show that R is an equivalence relation. Also, write all elements related to 4.

Let A={x in Z:0<=x<=12}. show that R={(a,b):a,b inbar(A),|a-b|is-:isib<=by4} is an equivalence relation.Find the set of all elements related to 1. Also write the equivalence class [2]

Prove that the relation R is the set A= {5,6,7,8,9,10} given by R= {(a, b) : |a - b| is divisible by 2} is an equivalence relation. Find the all elements related to the element 6.

Show that the relation R in the set A={x: x in N,x <=10} given by R={(a, b):a+ b is even number] is an equivalence relation. Also find the set of all elements related to 3

Show that the relation R on the set A={x in Z;0<=x<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

Prove that the relation R in the set A={5,6,7,8,9} given by R={(a,b):|a-b|, is divisible by 2}, is an equivalence relation.Find all elements related to the element 6.

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions

Show that the relation R in the set of real numbers, defined as R="...
Text Solution
|
Express the following matrix as the sum of a symmetric and skew symmet...
Text Solution
|
Show that the relation S in the set A={x\ \ Z\ :0\ lt=x\ lt=12} given ...
Text Solution
|
A family has 2 children. Find the probability that both are boys, i...
Text Solution
|
Find lambda if (2 hat i+6 hat j+14 hat k)xx\ ( hat i-\ lambda hat j+7...
Text Solution
|
Evaluate the following: int(x+2)/(sqrt((x-2)(x-3)))\ dx
Text Solution
|
Show that the differential equation ((x-y)dy)/(dx)=x+2y , is homoge...
Text Solution
|
In a certain college, 4% of boys and 1% of girls are taller than 1....
Text Solution
|
A company produces soft drinks that has a contract which requires t...
Text Solution
|
Find the vector equation of the plane passing through the points (2...
Text Solution
|
Evaluate the following int0^(3/2)|xcospix\ |\ dxdot
Text Solution
|
Find the area of the region in the first quadrant enclosed by x-a xi s...
Text Solution
|
Show that the altitude of the right circular cone of maximum volume ...
Text Solution
|
Solve for x: tan^(-1)3x+tan^(-1)2x=pi/4
Text Solution
|
Prove that: sin^(-1)(4/5)+sin^(-1)(5/(13))+sin^(-1)((16)/(65))=pi/2
Text Solution
|
If vecalpha=3 hat i+4 hat j+5 hat k and vecbeta=2 hat i+ hat j-\ 4 h...
Text Solution
|
Evaluate : int(cosx)/((2+sinx)dx\ (3+4sinx)
Text Solution
|
If [[1,2],[3,4]] [[3,1],[2,5]]=[[7,11],[k,23]], then write the value o...
Text Solution
|
Find the particular solution of the differential equation. (dy)/(dx...
Text Solution
|
Show that f\ : NvecN ,\ given by f(x)={x+1, if\ x\ i s\ od dx-1,\ \ ...
Text Solution
|