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Give an example to show that the relation R in the set of natural numbers, defined by \( R = ( (x,y), x, y \in\: N, x \leq \: y^2) \) is not transitive.
cbse
modelpaper
2012
sec-a
q1
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asked
Dec 26, 2012
by
thanvigandhi_1
edited
Jul 12, 2013
by
sreemathi.v
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Show that the relation R in the set R of real numbers, defined as \( R = {( a, b ) : a \leq b^2}\), is neither reflexive, nor symmetric , nor transitive.
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Let N be the set of natural numbers and R be the relation in N defined as \(R = {(a, b) : a = b – 2, b > 6}\). Then \[ \begin{array} ((A)\: (2, 4) ∈ R \quad & (B)\: (3, 8) ∈ R \\ (C) \: (6, 8) ∈ R \quad & (D)\: (8, 7) ∈ R. \end{array} \]
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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.
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Dec 26, 2012
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Give an example of relation which is reflexive but neither symmetric nor transitive.
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Jan 21, 2013
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Show that the relation \(R\) in the set {1,2,3} given by R={(1,2), (2,1)} is symmetric but neither reflexive nor transitive.
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Relation R in the set A = { 1, 2, 3, 4, 5, 6} defined as R = (x, y):y is divided by x}.
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Jan 10, 2013
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thanvigandhi_1
cbse
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