Question

if a = 1 2 3 4 its power set will contain​

Answer 1

Step-by-step explanation:

If S = {1,2,3}, then what is P(S) ? What is the power set of the set S = {1, 2, 3, 4} ? How many elements does the power set of S = {1, 2, 3, 4, 5, 6} have ?

The power set is the set of all subsets of a given set.

For the set S = {1,2,3} this means:

subsets with 0 elements: 0 (the empty set)

subsets with 1 element: {1}, {2}, {3}

subsets with 2 elements: {1,2}, {1,3}, {2,3}

subsets with 3 elements: S

Hence:

P(S) = {0, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, S}

Therefore, we have:

card(S) = 3 and card(P(S)) = 8 = 23

For the set S = {1,2,3,4} this means:

subsets with 0 elements: 0 (the empty set)

subsets with 1 element: {1}, {2}, {3}, {4}

subsets with 2 elements: {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}

subsets with 3 elements: {1,2,3}, {1,2,4}, {1,3,4} {2,3,4}

subsets with 4 elements: S

Therefore, we have:

card(S) = 4 and card(P(S)) = 16 = 24

Finally, if S = {1,2,3,4,5,6} then, based on the above examples, we would suspect that

card(S) = 6, therefore card(P(S)) = 26 = 64

Answer 2

Answer:

there will be 2×2×2×2=16 power sets

Step-by-step explanation:

2n

number of elements 4 so 2n=2 power of four

sets= {} {1} {2} {3} {4} {1,2} {2,3} {2,4} {3,4} {3,1} {4,1} {1,2,3} {1,2,4} {2,4,3} {1,2,3,4}