Are both the relations equivalent?


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relation is reflexive if (x,x)∈R 
relation is also symmetric as if (x,y)∈R this gives (y,x)∈R
relation is transitive  if (x,y)∈R,(y,z)∈R this gives (x,z)∈R
R1 is not reflexive i.e. |a - a| cannot be equal to 13 thus not equivalent
R2
reflexive since a -a = 0 is != 13
symmertic becuase  if | a -b | != 13, | b - a|  != 13
NOT transitive because
| a -b | ! = 13  = p
if | a -b | != 13   and | b -c | ! = 13 = q
| a - c | = p + q
p + q could be 13 i.e. | a -b | = 6, | b - c | = 7 both are not equal to 13
but the sum is equal to 13

Thus R1 and R2 are NOT equivalent relations
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