A partition pi of X = {a,b,c,d} is given bypi = {{a,c,d},{b}}.Which ordered pairs are in the equivalence relation p determined by the partition? A (a,a) B (a,b) C (a,c) D (a,d) E (b,a) F (b,b) G (b,c) H (b,d) I (c,a) J (c,b) K (c,c) L (c,d) M (d,a) N (d,b) O (d,c) P (d,d) Q None of them
Question
A partition pi of X = {a,b,c,d} is given bypi = {{a,c,d},{b}}.Which ordered pairs are in the equivalence relation p determined by the partition? A (a,a) B (a,b) C (a,c) D (a,d) E (b,a) F (b,b) G (b,c) H (b,d) I (c,a) J (c,b) K (c,c) L (c,d) M (d,a) N (d,b) O (d,c) P (d,d) Q None of them
Solution
Para determinar los pares ordenados en la relación de equivalencia p determinada por la partición pi = {{a,c,d},{b}}, debemos identificar los elementos que pertenecen al mismo subconjunto en la partición.
- El subconjunto {a,c,d} contiene los elementos a, c y d.
- El subconjunto {b} contiene el elemento b.
Los pares ordenados en la relación de equivalencia p son aquellos donde ambos elementos pertenecen al mismo subconjunto.
Para el subconjunto {a,c,d}:
- (a,a)
- (a,c)
- (a,d)
- (c,a)
- (c,c)
- (c,d)
- (d,a)
- (d,c)
- (d,d)
Para el subconjunto {b}:
- (b,b)
Entonces, los pares ordenados en la relación de equivalencia p son: A (a,a), C (a,c), D (a,d), F (b,b), I (c,a), K (c,c), L (c,d), M (d,a), O (d,c), P (d,d).
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