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 T with sides 3,4 and 5 ?
I had understanded that relation is equivalence but not it's second step. explain second step and solve it please.
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R=(P1,P2)they have the same number of sides
R is reflexive since(P1,P1)belongs to R have same polygon and have same number of sides with itself.
let (P1,P2) belongs R.
implies P1 and P2 have same no. of sides
implies P2 and P1 have same no. of sides
implies (P2,P1) belongs R.
therefore R is symmetric.
let (P1,P2) and (P2,P3) belongs R
THEY ALL HAVE SAME NO. OF SIDES.
therefore here R is transitive
thats why its an equivalence relation.
THE SET OF ALL ELEMENTS RELATED TO TRIANGLE IS THE SET OF ALL TRIANGLES.
R is reflexive since(P1,P1)belongs to R have same polygon and have same number of sides with itself.
let (P1,P2) belongs R.
implies P1 and P2 have same no. of sides
implies P2 and P1 have same no. of sides
implies (P2,P1) belongs R.
therefore R is symmetric.
let (P1,P2) and (P2,P3) belongs R
THEY ALL HAVE SAME NO. OF SIDES.
therefore here R is transitive
thats why its an equivalence relation.
THE SET OF ALL ELEMENTS RELATED TO TRIANGLE IS THE SET OF ALL TRIANGLES.
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can you explain last two lines of your answer
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THE LAST 2 LINES;
the elements in A related to right angled triangle T with sides 3,4,5 are those polygons which have 3 sides (since T is a polygon with 3 sides).HENCE THE SET OF TRIANGLES IN A RELATED TO TRIANGLE T IS THE SET OF TRIANGLES. HOPE U UNDERSTAND. THANKYOU...................
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