I need Step by step Solutions, An equivalence relation R, is defined on the set

Question

I need Step by step Solutions,

An equivalence relation R, is defined on the set R2 as follows: (x,y)R{x',y') doublearrow [x] = [x'] and [y] = [y'] Here, for any real number x, the number [x] is defined as the least integer that is greater than or equal to x. For example, [-2] = -2, [ -1.8] = -1, and [2.6] = 3. Which of the following elements of R2 belong to the equivalence class of (1.2, -2.8) with respect to R: (1.3, -2.1), (1.6, -3.1), (1, -3), (2,2), (0.2, -0.8), (1, -2), (2, -3), (2, -2), (-0.2,0.8) Give a geometric description of the equivalence class [(1.2, -2.8)]R.

Explanation / Answer

(1.2,-2.8)

so [1.2] = 2 and [-2.8]=-2

a)(1.3,-2.1); [1.3] = 2 and [-2.1]=-2. so this belongs

(1.6,-3.1);[1.6]=2 and [-3.1]=-3 . NO

(1,-3); [1]=1 and [-3]=-3; NO

(2,2) NO

(0.2,-0.8) NO
(1,-2) NO

(2,-3)NO

(2,-2)YES

(-0.2,0.8) NO

b)[1.2,-2.8]

The geomwtric distribitution will be 1<=x<2 and -2<=y<-3

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