Giving that
A={1,2,3,4}find
(a).p{a}
(b). n[p(a)]
(a) p{a} represents the power set of set A. The power set is the set of all possible subsets of A, including the empty set and the set itself.
In this case, the power set of A={1,2,3,4} would be:
p{A} = { {}, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}, {1,2,3,4} }
(b) n[p(a)] represents the number of elements in the power set of A.
In this case, the number of elements in the power set of A is:
n[p(A)] = 2^4 = 16
To find the power set of set A={1,2,3,4}, we need to find all possible subsets of A.
(a) Finding P(A):
Step 1: Write down all the individual elements of set A: {1, 2, 3, 4}.
Step 2: Now, take the individual elements and start forming subsets of size 1. In this case, we have subsets of size 1 as {1}, {2}, {3}, and {4}.
Step 3: Next, form subsets of size 2 by combining 2 elements. For A, we have subsets of size 2 as {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, and {3, 4}.
Step 4: Continue this process for subsets of size 3 and 4. For A, we have subsets of size 3 as {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, and {2, 3, 4}.
Step 5: Finally, include the empty set {} and the original set A itself, which gives us P(A) = { {}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4} }.
(b) Finding the number of elements in P(A):
To find the number of elements in P(A), we simply count the number of subsets.
In this case, P(A) has 2^4 = 16 elements.
To find the power set of set A={1,2,3,4}, we need to consider all possible subsets of set A, including the empty set and the set itself.
(a) To find p(A), we start by making a list of all possible subsets of A.
Subset 1: {}
Subset 2: {1}
Subset 3: {2}
Subset 4: {3}
Subset 5: {4}
Subset 6: {1,2}
Subset 7: {1,3}
Subset 8: {1,4}
Subset 9: {2,3}
Subset 10: {2,4}
Subset 11: {3,4}
Subset 12: {1,2,3}
Subset 13: {1,2,4}
Subset 14: {1,3,4}
Subset 15: {2,3,4}
Subset 16: {1,2,3,4}
Therefore, p(A) = {{}, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}.
(b) To find n[p(A)], we count the number of subsets in p(A).
Since p(A) has 16 subsets, n[p(A)] = 16.