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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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Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b): both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset{1, 3, 5, 7} are related to each other and all elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7}} is related to any element of the subset {2, 4, 6}.
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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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Let L be the set of all lines in XY - planes and R be the relation in L defined as R = \( { (L_1, L_2 ) : L_1 \: is \: parallel\: to\: L_2} \). Show the R is an equivalence relation. Find the set of all the lines related to the line \( y=2x+4.\)
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Jan 11, 2013
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Show that the R defined on the set A of all triangles as $R = \{(T_1, T_2): T_1$ is similar to $T_2 \}$ is an equivalence relation. Consider three right-angled triangles \( T_1\) with sides 3, 4, 5, \( T_2\) with sides 5, 12, 13 and \( T_3\) with sides 6, 8, 10. Which triangles among \( T_1, T_2 and T_3\) are related?
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