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If A = {a, b, c, d} list the element of power set P(A)
- a){ ? {a} {b} {c} {d} {a, b} {a, c} {a, d} {b, c} {b, d} {c, d}
- b){a, b, c} {a, b, d} {a, c, d} {b, c, d}
- c){a, b, c, d}
- d)All the above elements are in P(A)
Correct answer is option 'D'. Can you explain this answer?
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If A = {a, b, c, d} list the element of power set P(A)a){ ? {a} {b} {c...
Power Set:
The power set of a set A, denoted as P(A), is the set of all possible subsets of A, including the empty set and the set itself. In other words, it is the collection of all possible combinations of elements in A.
Given Set:
A = {a, b, c, d}
Calculating Power Set:
To calculate the power set of A, we need to list all possible subsets of A.
1. Empty Set
- The empty set is a subset of every set, including A.
- Symbolically represented as {} or Ø.
2. Individual Elements
- Each individual element of A is also a subset of A.
- {a}, {b}, {c}, {d}
3. Two-Element Subsets
- We consider subsets with two elements, which can be formed by selecting any two elements from A.
- {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}
4. Three-Element Subsets
- Similarly, we consider subsets with three elements, which can be formed by selecting any three elements from A.
- {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}
5. Four-Element Subset
- The entire set A itself is also a subset of A.
- {a, b, c, d}
Power Set P(A):
Combining all the subsets obtained above, we get the power set of A, P(A):
{ {}, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, c, d} }
Correct Answer:
Option D, which states that all the above elements are in P(A), is the correct answer.
The power set of a set A, denoted as P(A), is the set of all possible subsets of A, including the empty set and the set itself. In other words, it is the collection of all possible combinations of elements in A.
Given Set:
A = {a, b, c, d}
Calculating Power Set:
To calculate the power set of A, we need to list all possible subsets of A.
1. Empty Set
- The empty set is a subset of every set, including A.
- Symbolically represented as {} or Ø.
2. Individual Elements
- Each individual element of A is also a subset of A.
- {a}, {b}, {c}, {d}
3. Two-Element Subsets
- We consider subsets with two elements, which can be formed by selecting any two elements from A.
- {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}
4. Three-Element Subsets
- Similarly, we consider subsets with three elements, which can be formed by selecting any three elements from A.
- {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}
5. Four-Element Subset
- The entire set A itself is also a subset of A.
- {a, b, c, d}
Power Set P(A):
Combining all the subsets obtained above, we get the power set of A, P(A):
{ {}, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, c, d} }
Correct Answer:
Option D, which states that all the above elements are in P(A), is the correct answer.
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If A = {a, b, c, d} list the element of power set P(A)a){ ? {a} {b} {c...
D
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If A = {a, b, c, d} list the element of power set P(A)a){ ? {a} {b} {c} {d} {a, b} {a, c} {a, d} {b, c} {b, d} {c, d}b){a, b, c} {a, b, d} {a, c, d} {b, c, d}c){a, b, c, d}d)All the above elements are in P(A)Correct answer is option 'D'. Can you explain this answer?
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