Let A = {1,2,3,4,5} and X = P(A) be its powerset. Define a
binary relation on...
Let A = {1,2,3,4,5} and X = P(A) be its powerset. Define a
binary relation on X by for any sets S, T ∈ X, S∼T if and only if S
⊆ T.
(a) Is this relation reflexive?
(b) Is this relation symmetric or antisymmetric?
(c) Is this relation transitive?
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
Let R be the relation on the set A = {1,2,3,4,5} where aRb
exactly when |a−b|...
Let R be the relation on the set A = {1,2,3,4,5} where aRb
exactly when |a−b| = 1. Let S be the relation on the set A where
aSb exactly when a = 1 or b = 4. 1. Find matrix representations and
digraph representations for both R and S. 2. Find matrix
representations for ¯ R and S^−1. 3. Find digraph representations
for R∩S and R◦S.
Determine whether the relation R is reflexive, symmetric,
antisymmetric, and/or transitive [4 Marks]
22
The relation...
Determine whether the relation R is reflexive, symmetric,
antisymmetric, and/or transitive [4 Marks]
22
The relation R on Z where (?, ?) ∈ ? if ? = ? .
The relation R on the set of all subsets of {1, 2, 3, 4} where
SRT means S C T.
Prove that if the relation R is symmetric, then its transitive
closure, t(R)=R*, is also symmetric....
Prove that if the relation R is symmetric, then its transitive
closure, t(R)=R*, is also symmetric. Please provide step by step
solutions
Disprove: The following relation R on set Q is either reflexive,
symmetric, or transitive. Let t...
Disprove: The following relation R on set Q is either reflexive,
symmetric, or transitive. Let t and z be elements of Q. then t R z
if and only if t = (z+1) * n for some integer n.