- #1
Bonafide
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Hello!
I'm a bit lost on these questions pertaining to equivalence relations/classes. If someone could run me through either, or both, of these questions, I'd be very thankful! I'm completely lost as to what to do with the z in terms of set S...
Show that the given relation R is an equivalence relation on set S. Then describe the equivalence class containing the given element z in S, and determine the number of distinct equivalence clases of R.
16. Let S be the set of all subsets of {1,2,3,4,5}. let z = {1,2,3}, and define xRy to mean that x [tex]\bigcap[/tex] {1,3,5} = y [tex]\bigcap[/tex] {1,3,5}.
18. Let S be the set of ordered pairs or real numbers, let z = (3, -4) and define (x1, x2) R (y1, y2) means that x1 + y2 = y1 + x2.
I'm a bit lost on these questions pertaining to equivalence relations/classes. If someone could run me through either, or both, of these questions, I'd be very thankful! I'm completely lost as to what to do with the z in terms of set S...
Homework Statement
Show that the given relation R is an equivalence relation on set S. Then describe the equivalence class containing the given element z in S, and determine the number of distinct equivalence clases of R.
16. Let S be the set of all subsets of {1,2,3,4,5}. let z = {1,2,3}, and define xRy to mean that x [tex]\bigcap[/tex] {1,3,5} = y [tex]\bigcap[/tex] {1,3,5}.
18. Let S be the set of ordered pairs or real numbers, let z = (3, -4) and define (x1, x2) R (y1, y2) means that x1 + y2 = y1 + x2.