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Let N be the set of all natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad = bc. Show that R is an equivalence relation.
cbse
modelpaper
2012
sec-b
q11
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asked
Dec 26, 2012
by
thanvigandhi_1
edited
Jul 12, 2013
by
sreemathi.v
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Let N denote the set of all natural numbers and R be the relation on N x N defined by $ (a,b)R(c,d) \Leftrightarrow ad(b + c) = bc(a + d).$ Show that R is an equivalence relation on N x N.
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If R is a relation in N x N, show that the relation R defined by : (a, b)R(c, d)if and only if ad = bc is an equivalence relation.
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Show that the relation R defined by (a, b ) R ( c, d ) \( \Rightarrow \) a + b + c on the set N x N is an equivalence relation.
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Show that the relation R : N \( \rightarrow \) N defined by (a,b)R(c,d) \( \iff \) a+d = b+c for all (a,b), (c,d) \( \in \) N x N is an equivalence relation.
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