Let R be a relation on a set A Let R' be the relation on A defined by Graph(R') = (A × A) – Graph(R). (a) If R is reflexive, is R' necessarily reflexive, necessarily not re- flexive or not necessarily either? As always, justify your answer. (b) If R is symmetric, is R' necessarily symmetric, necessarily not symmetric, or not necessarily either. As always, justify your answer. 1
Let R be a relation on a set A Let R' be the relation on A defined by Graph(R') = (A × A) – Graph(R). (a) If R is reflexive, is R' necessarily reflexive, necessarily not re- flexive or not necessarily either? As always, justify your answer. (b) If R is symmetric, is R' necessarily symmetric, necessarily not symmetric, or not necessarily either. As always, justify your answer. 1
Advanced Engineering Mathematics
10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:OLet R be a relation on a set A Let R' be the relation on A defined
by Graph(R') = (A × A) – Graph(R).
(a) If R is reflexive, is R' necessarily reflexive, necessarily not re-
flexive or not necessarily either? As always, justify your answer.
(b) If R is symmetric, is R' necessarily symmetric, necessarily not
symmetric, or not necessarily either. As always, justify your
answer.
1
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