For each of the following relations, determine whether the relation is: Reflexive. Transitive. A partial order. • A strict order. Anti-reflexive. Symmetric. Anti-symmetric. An equivalence relation. ustify all your answers. R is a relation on the set of all people such that (a, b) e R if and only if a and b have a common grandparent.
answer all the question
For each of the following relations, determine whether the relation is:
• Reflexive.
• Anti-reflexive.
• Symmetric.
• Anti-symmetric.
• Transitive.
• A partial order.
• A strict order.
• An equivalence relation.
Justify all your answers.
a. ? is a relation on the set of all people such that (?, ?) ∈ ? if and only if ? and ? have a common grandparent.
b. ? is a relation on the power set of a set ? such that (?, ?) ∈ ? if and only if ? ⊂ ?.
c. ? is a relation on ℤ such that (?, ?) ∈ ? if and only if ?? ≥ ?.
d. ? is a relation on ℤ + such that (?, ?) ∈ ? if and only if there is a positive integer ? such that ?^? = ?.
e. ? is a relation on ℝ such that (?, ?) ∈ ? if and only if ? − ? is rational. Hint: The sum of two rational numbers is rational.
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