Match the following columns.
Column I | Column II | ||
(A) | (P) | Reflexive | |
(B) | (Q) | Symmetric | |
(C) | (R) | ||
(D) |
| (S) | Equivalence |
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
→ (R); → (Q); → (P); → (P, Q, R, S)
,
So, 
is not reflexive.
Now, 
is not symmetric.
Let 
and 
and 
is transitive.
So, each element of 
is not related to itself by the relation 
.
is not reflexive.
Now, 
is symmetric relation.
Now, let 
and 
is not transitive.
or 
So, 
is reflexive.
Let 
and 
is not symmetric.
Now, let 
and 
and 
Then, 
is not transitive.
is reflexive.
Now, 
is symmetric.
Now, let 
and 
…….. (i)
[using Eq. (i)]
is transitive.
Hence, 
is an equivalence relation.
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