Let
A be the set of all integers, and let R be the relation "m divides...
Let
A be the set of all integers, and let R be the relation "m divides
n." Determine whether or not the given relation R, on the set A, is
reflexive, symmetric, antisymmetric, or transitive.
There is no equivalence relation R on set {a, b, c, d,
e} such that R...
There is no equivalence relation R on set {a, b, c, d,
e} such that R contains less than 5 ordered pairs (True or
False)
Let P be the set of all ordered pairs (a, b) where a and b are...
Let P be the set of all ordered pairs (a, b) where a and b are
real numbers. Let us define a two-place relation ≡ on P by (a, b) ≡
(c, d) if and only if a^2 − c^2 = 2b − 2d where (a, b) and (c, d)
belong to P. Prove that ≡ is an equivalence relation on P. Draw a
diagram on the X × Y plane of the equivalence class that contains
the point (2,...
2. Define a relation R on pairs of real numbers as follows: (a,
b)R(c, d) iff...
2. Define a relation R on pairs of real numbers as follows: (a,
b)R(c, d) iff either a < c or both a = c and b ≤ d. Is R a
partial order? Why or why not? If R is a partial order, draw a
diagram of some of its elements.
3. Define a relation R on integers as follows: mRn iff m + n is
even. Is R a partial order? Why or why not? If R is...
Let A = {1,2,3}. Determine all the equivalence relations R on A.
For each of these,...
Let A = {1,2,3}. Determine all the equivalence relations R on A.
For each of these, list all ordered pairs in the relation
Are the following vector space and why?
1.The set V of all ordered pairs (x, y)...
Are the following vector space and why?
1.The set V of all ordered pairs (x, y) with the addition of
R2, but scalar multiplication a(x, y) = (x, y) for all a
in R.
2. The set V of all 2 × 2 matrices whose entries sum to 0;
operations of M22.
Determine whether the given relation is an equivalence relation
on {1,2,3,4,5}. If the relation is an...
Determine whether the given relation is an equivalence relation
on {1,2,3,4,5}. If the relation is an equivalence relation, list
the equivalence classes (x, y E {1, 2, 3, 4, 5}.)
{(1,1), (2,2), (3,3), (4,4), (5,5), (1,3), (3,1), (3,4),
(4,3)}
If the relation above is not an equivalence relation, state that
the relation is not an equivalence relation and why.
Example: "Not an equivalence relation. Relation is not
symmetric"
Remember to test all pairs in relation R