Give the smallest equivalence relation r on a containing the pairs (a, c), (a, e), and (b, d) (i. e., the equivalence relation r containing the given pairs with the fewest number of elements). what are the equivalence classes of your relation r from part i? let s be the relation on the set of integers such that xsy if and only if x2 ≡2 y2. in other words, s = { (x, y) ∈ z × z | x2 ≡2 y2 }. show that s is an equivalence relation. what are the equivalence classes of s?

answer: 12

step-by-step explanation:

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

c

step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq