if R is the set of all relations defined on A and E is the set of all functions defined on A then
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Step-by-step explanation:
R is reflexive since (P
1
,P
1
)∈R as the same polygon has the same number of sides with itself.
Let (P
1
,P
2
)∈R.
⇒P
1
and P
2
have the same number of sides.
⇒P
2
and P
1
have the same number of sides.
⇒(P
2
,P
1
)∈R
∴R is symmetric.
Now,
Let (P
1
,P
2
),(P
2
,P
3
)∈R.
⇒P
1
and P
2
have the same number of sides. Also, P
2
and P
3
have the same number of sides.
⇒P
1
and P
3
have the same number of sides.
⇒(P
1
,P
3
)∈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.
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