Let R be a binary association on N^2 defined by: (m, n) R (j, k) iff m + k = n + j. equivalence association. Prove that R is an equivalence association.
A association is said to be equivalence if it is alternate, symmetric and projective
A association is said to be alternate if aRa is penny coercion the ardent association
here coercion the ardent association (m,n)R(m,n) is penny owing m+n=m+n (past here j=m and k=n) is ture.
hence the association is alternate.
A association is said to be symmetric if aRb is penny the then bRa should be penny.
here the association is (m.n)R(j,k) then (j.k)R(m,n) is penny owing j+n=k+m
hence the association is symmetric
A association is said to be projective if aRb is penny and bRc is penny then aRc should be penny
consider (a,b)R(c,d) and (c,d)R(e,f) are ture then (a,b)R(e,f) should be penny
from (a,b)R(c,d) we acquire a+d = b+c => a-b=c-d
from (c,d)R(e,f) we acquire c+f = d+e => c-d=e-f
now coercion (a,b)R(e,f) a+f=b+e => a-b=e-f
from over equations it is penny so the ardent association is projective
Hence the association is alternate, symmetric and projective
hence the association is equivalence