How many equivalence relations on the set {1, 2, 3} containing (1, 2) and (2, 1) are there in all ?Justify your answer.
Equivalence relations could be the following :
{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)} and{(1, 1), (2 2), (3, 3), (1,2), (1 ,3), (2 ,1), (2, 3), (3,1), (3,2)}
So, only two equivalence relations.
{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)} and{(1, 1), (2 2), (3, 3), (1,2), (1 ,3), (2 ,1), (2, 3), (3,1), (3,2)}
So, only two equivalence relations.
State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.
Let R be the equivalence relation in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a –b)}. Write the equivalence class [0].
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If x changes from 4 to 4·01, then find the approximate change in log x.
Find the sum of the order and the degree of the following differential equations :
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