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Some examples from this set of practice questions
1.
What does the term \"reflexive\" mean?
Answer: A relation R on a set A is reflexive if for all x in A, xRx holds.
2.
What does the term \"irreflexive\" mean?
Answer: A relation R on a set A is irreflexive if for all x in A, xRx does not hold.
3.
What does the term \"symmetric\" mean?
Answer: A relation R on a set A is symmetric if for all x and y in A, xRy implies yRx holds.
4.
What does the term \"antisymmetric\" mean?
Answer: A relation R on a set A is antisymmetric if for all x and y in A, (xRy and yRx) implies that x = y holds.
5.
What does the term \"transative\" mean?
Answer: A relation R on a set A is transative if for all x, y and z in A, (xRy and yRz) implies that xRz holds.
6.
What is an equivalence relation?
Answer: An equivalence relation is a relation that is reflexive, symmetric and transative.
7.
What is an ordering relation?
Answer: An ordering relation is a relation that is reflexive, antisymmetric and transative.
8.
What is a partially ordered set?
Answer: A partially ordered set (poset) is a pair of a set and ordering relation (X, R) with X as the set and R as the ordering relation and is denoted as ≤.
9.
What is a total ordering?
Answer: A total ordering is a partially ordered set (poset) in which any two elements are comparable. Each partial ordering can be extended to a linear ordering.
10.
What is an embedding?
Answer: An embedding is a mapping f: X -> X\' of (X, ≤) into (X\', ≤\') if the following holds: - f is injective - f(x) ≤\' f(y) if and only if x ≤ y
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