If relation R : (a, b) R(c, d) is only if ad – bc is divisible by 5 (a, b, c, d Î Z) then Ris
If relation R : (a, b) R(c, d) is only if ad – bc is divisible by 5 (a, b, c, d Î Z) then Ris
Option 1 -
Reflexive
Option 2 -
Symmetric, Reflexive but not Transitive
Option 3 -
Reflexive, Transitive but not symmetric
Option 4 -
Equivalence relation
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1 Answer
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Correct Option - 2
Detailed Solution:Reflexive :for (a, b) R (a, b)
-> ab– ab = 0 is divisible by 5.
So (a, b) R (a, b) " a, b Î Z
R is reflexive
Symmetric:
For (a, b) R (c, d)
If ad – bc is divisible by 5.
Then bc – ad is also divisible by 5.
-> (c, d) R (a, b) "a, b, c, dÎZ
R is symmetric
Transitive:
If (a, b) R (c, d) ->ad –bc divisible by 5 and (c, d) R (e, f) Þcf – de divisible by 5
ad – bc = 5k1 k1 and k2 are integers
cf– de = 5k2
afd – bcf = 5k1f
bcf – bde = 5k2b
afd – bde = 5 (k1f + k2b)
d (af– be) = 5 (k1f + k2b)
-> af – be is not divisible by 5 for every a, b,
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