Define a relation T on R as follows: for all x and y in R, x T y if and only if x^2 = y^2. Then T is an equivalence relation on R.
(a) Prove that T is an equivalence relation on R.
(b) Find the distinct equivalence classes of T.
Mathematics
You might also like to view...
Consider only the discriminant, b2 - 4ac, to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.x2 + 5x + 1 = 0
A. One real solution B. Two different real-number solutions C. Two different imaginary-number solutions
Mathematics
Convert the numeral to Hindu-Arabic form.
A. 34,213 B. 31,333 C. 34,233 D. 34,460
Mathematics
Evaluate the integral.
A. -3 ln 2 B. 6 ln 2 C. 3 ln 2 D. 3 ln 3
Mathematics
The table below shows Joe's golf scores from Saturday.
The total number of holes of golf Joe played on Saturday was
A. 8. B. 80. C. 153. D. 36. E. none of these
Mathematics