Short Answer Type(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y) : x and y work at the same place}
(b) R = {(x,y) : x and y live in the same locality}
(c) R = {(x, y) : x is exactly 7 cm taller than y}
(d) R = {(x, y) : x is wife of y}
(e) R = {(x,y) : x is father of y}
Let A = {1,2,3}
Then A x A = {(1,1), (1,2), (1, 3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
Let R = {(1,1), (1,2), (2,1), (2,2)}.
R is not reflexive as 3∈ A and (3,3) ∉ R.
R is symmetric as (a, b) ∈ R ⇒ (b, a) ∈R.
R is transitive since (a, b) ∈ R and (b, c) ∈R implies that (a, c) ∈ R.
Show that the relation R defined in the set A of all triangles as R = {(T1, T2) : T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with Sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8. 10. Which triangles among T1, T2 and T3 are related ?
Long Answer Type
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