Show that the relation R defined in the set A of all polygons as R={(P1,P2):P3 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?

Question

Show that the relation R defined in the set A of all polygons as R={(P1​,P2​):P3​ 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?

Filo · Accepted Answer

(P,P)∈R as P and P have sane number of sides hence R is reflexive.(P,Q)∈R⇒P and Q have same number of sides ⇒Q and P have same number of sides ⇒(Q,P)∈Rhence R is symmetric (P,Q)∈R and (Q,R)∈R⇒P and Q have number of sides, Q and R have same number of sides. P and R have same number of sides ⇒(P,R)∈Rhence R is transitive ∴R is an equivalence Relation T is a Triangle (P,T)∈R⇒P and T have same number of sides ⇒P is also a triangle ∴ set of all elements related as T is the set of all triangle in A.

Question Text	Show that the relation $R$ defined in the set $A$ of all polygons as $R = {(P_{1}, P_{2}) : P_{3} an d P_{2} ha v e s am e n u mb er o f s i d es}$ , 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 $5$ ?
Answer Type	Text solution:1
Upvotes	150

Show that the relation $R$ defined in the set $A$ of all polygons as $R = {(P_{1}, P_{2}) : P_{3} an d P_{2} ha v e s am e n u mb er o f s i d es}$ , 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 $5$ ?

Text solutionVerified

Practice questions from similar books

Show that the relation R defined in the set A of all polygons as R={(P1​,P2​):P3​ 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?

Text solutionVerified

Practice questions from similar books

Show that the relation $R$ defined in the set $A$ of all polygons as $R = {(P_{1}, P_{2}) : P_{3} an d P_{2} ha v e s am e n u mb er o f s i d es}$ , 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 $5$ ?