Date: Wed, 05 May 1999 11:12:41 -0500 Subject: equivalent relations I am tutoring a boy who got this assignment from his teacher and I have no clue how to do it because I don't even know what the questions is asking! I need some help. Hereit is: "Give five examples of relations which are not equivalent relations and five examples of equivalent relations and explain why they are equivalent relations." This is seventh grade and I read about it in his book but it is not coming together for me. HELP!!! Megan Hi Megan
RELATIONS AND EQUIVALENCE RELATIONS - x is related to y if "x and y have the same decimal value". So here 1/2
is related to 2/4. Also 2/4 is related to 1/2.
- x is related to y if "x is bigger than y". Here 5 is related to 3 but 3
is not related to 5. (This example shows that the technical notion of
"related" in mathematics might ressemble our intuitive notion of a
relationship, but they differ when it comes to details: among people, if a
is related to b then necessarily b is related to a.)
- x and y are related if x^2 + y^2 = 1
- x and y are related if x + y < 1.
The technical definition:
Examples using sets of numbers: - Two fractions are equivalent if they equal the same decimal number. (or
easier, a/b is equivalent to c/d if ad = bc.) (This is the only one of the
examples in the list of relations given above that happens to be an
equivalence relation.)
- Two counting numbers are equivalent if they have the same parity -- that
is if they are both even or both odd. Here 4 is related to 6 (since both
are even) but not to 7.
- Two counting numbers are equivalent if they leave the same remainder
after division by 3. Here 4 is related to 7 (since both are 1 more than a
multiple of 3) but not to 6.
- Throw numbers randomly into boxes. Say that two numbers are equivalent
when they are in the same box.
- Equality is a very special equivalence relation. An number is equal only to itself and not to any other number. (It amounts to the box example #4 with exactly 1 number in every box.)
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