Which of the following sets is equal to the power set of G = {x, y}?
Practice Questions
1 question
Q1
Which of the following sets is equal to the power set of G = {x, y}?
{∅, {x}, {y}, {x, y}}
{x, y}
{∅, {x, y}}
{x, y, ∅}
The power set of a set with n elements has 2^n subsets. For G, n=2, so the power set is {∅, {x}, {y}, {x, y}}.
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following sets is equal to the power set of G = {x, y}?
Solution: The power set of a set with n elements has 2^n subsets. For G, n=2, so the power set is {∅, {x}, {y}, {x, y}}.
Steps: 6
Step 1: Identify the set G. In this case, G = {x, y}.
Step 2: Count the number of elements in G. There are 2 elements: x and y.
Step 3: Use the formula for the power set. The power set of a set with n elements has 2^n subsets.
Step 4: Calculate 2^n. Since n = 2, calculate 2^2 = 4.
Step 5: List all the subsets of G. The subsets are: the empty set ∅, the set with just x {x}, the set with just y {y}, and the set with both x and y {x, y}.
Step 6: Combine the subsets into the power set. The power set of G is {∅, {x}, {y}, {x, y}}.
