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Show that the Relation R Defined in the Set a of All Polygons as R = {(P1, P2): P1 and P2 Have Same Number of Sides}, is an Equivalence Relation. What is the Set of All Elements in a Related to the Right Angle Triangle T with Sides 3, 4 and 5? - Mathematics

Show that the relation R defined in the set A of all polygons as R = {(P1P2): P1 and P2have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

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Solution

R = {(P1P2): P1 and P2 have same the number of sides}

R is reflexive since (P1P1) ∈ R as the same polygon has the same number of sides with itself.

Let (P1P2) ∈ R.

⇒ P1 and P have the same number of sides.

⇒ P2 and P1 have the same number of sides.

⇒ (P2P1) ∈ R

∴R is symmetric.

Now,

Let (P1P2), (P2P3) ∈ R.

⇒ P1 and P2 have the same number of sides. Also, P2 and P3 have the same number of sides.

⇒ P1 and P3 have the same number of sides.

⇒ (P1P3) ∈ R

∴R is transitive.

Hence, R is an equivalence relation.

The elements in A related to the right-angled triangle (T) with sides 3, 4, and 5 are those polygons which have 3 sides (since T is a polygon with 3 sides).

Hence, the set of all elements in A related to triangle T is the set of all triangles.

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 12 Maths
Chapter 1 Relations and Functions
Q 13 | Page 6
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