17. Show that the relation S in the set A = (x E 2:0 SXS 121 given by
S = (a, b): a, b e A, la - bl is divisible by 4) is an equivalence relation.
Find the set of elements related to 1.
Answers
The set of elements related to 1 is {1}.
Step-by-step explanation:
12th
Maths
Relations and Functions
Types of Relations
Show that each of the relat...
MATHS
Show that each of the relation R in the set A={x∈Z:0≤x≤12}, given by is an equivalence relation. Find the set of all elements related to 1 in each case.
R={(a,b):a=b}
May 01, 2020
avatar
Muhammad D'Souza
Share
Save
ANSWER
A={x∈Z:0≤x≤12}={0,1,2,3,4,......,11,12}
R={(a,b):a=b}={(0,),(1,1),(2,2),........,(11,11),(12,12)}
For any element a∈A, we have (a,a)∈R, since a=a.
∴R is reflexive.
Now, let (a,b)∈R.
⇒a=b
⇒b=a
⇒(b,a)∈R
∴R is symmetric.
Now, let (a,b)∈R and (b,c)∈R.
⇒a=b and b=c
⇒a=c
⇒(a,c)∈R
∴R is transitive.
Hence, R is an equivalence relation.
The elements in R that are related to 1 will be those elements from set A which are equal to 1.
Hence, the set of elements related to 1 is {1}.