To create the symmetric closure $ p^s $ of the empty relation $ p = \emptyset $ on the set $ X = \{a, b, c, d\} $, we need to follow these steps:

1. **Identify the empty relation**: The given relation $ p $ is empty, meaning it contains no ordered pairs.

2. **Understand symmetric closure**: The symmetric closure of a relation $ p $ is the smallest symmetric relation that contains $ p $. A relation is symmetric if for every $ (x, y) \in p $, the pair $ (y, x) $ is also in $ p $.

3. **Add pairs to make it symmetric**: Since $ p $ is empty, there are no pairs to consider. Therefore, the symmetric closure of an empty relation is also an empty relation.

4. **Result**: The symmetric closure $ p^s $ of the empty relation $ p $ on the set $ X $ is still an empty relation. No ordered pairs need to be added.

Thus, the ordered pairs that need to be added to the empty relation $ p = \emptyset $ to create the symmetric closure $ p^s $ are none. The symmetric closure remains $ \emptyset $.

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To create the symmetric closure $ p^s $ of the empty relation $ p = \emptyset $ on the set $ X = \{a, b, c, d\} $, we need to follow these steps:

1. **Identify the empty relation**: The given relation $ p $ is empty, meaning it contains no ordered pairs.

2. **Understand symmetric closure**: The symmetric closure of a relation $ p $ is the smallest symmetric relation that contains $ p $. A relation is symmetric if for every $ (x, y) \in p $, the pair $ (y, x) $ is also in $ p $.

3. **Add pairs to make it symmetric**: Since $ p $ is empty, there are no pairs to consider. Therefore, the symmetric closure of an empty relation is also an empty relation.

4. **Result**: The symmetric closure $ p^s $ of the empty relation $ p $ on the set $ X $ is still an empty relation. No ordered pairs need to be added.

Thus, the ordered pairs that need to be added to the empty relation $ p = \emptyset $ to create the symmetric closure $ p^s $ are none. The symmetric closure remains $ \emptyset $.

Knowee AI · Accepted Answer

To create the symmetric closure $ p^s $ of the empty relation $ p = \emptyset $ on the set $ X = \{a, b, c, d\} $, we need to follow these steps:

1. **Identify the empty relation**: The given relation $ p $ is empty, meaning it contains no ordered pairs.

2. **Understand symmetric closure**: The symmetric closure of a relation $ p $ is the smallest symmetric relation that contains $ p $. A relation is symmetric if for every $ (x, y) \in p $, the pair $ (y, x) $ is also in $ p $.

3. **Add pairs to make it symmetric**: Since $ p $ is empty, there are no pairs to consider. Therefore, the symmetric closure of an empty relation is also an empty relation.

4. **Result**: The symmetric closure $ p^s $ of the empty relation $ p $ on the set $ X $ is still an empty relation. No ordered pairs need to be added.

Thus, the ordered pairs that need to be added to the empty relation $ p = \emptyset $ to create the symmetric closure $ p^s $ are none. The symmetric closure remains $ \emptyset $.

Which ordered pairs need to be added to the empty relationp = {}on the set X = {a,b,c,d} to create the symmetric closure p^s of p?

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