If B = {a, b, c, d}, what is the power set of B?

{∅, {a}, {b}, {c}, {d}}
{∅, {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}}
{∅, {a, b}, {c, d}}
{∅, {a, b, c}, {d}}

If B = {a, b, c, d}, what is the power set of B?

Correct Answer: { {}, {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} }

Step 1: Identify the set B. In this case, B = {a, b, c, d}.
Step 2: Count the number of elements in set B. There are 4 elements: a, b, c, and d.
Step 3: Use the formula for the power set, which is 2^n, where n is the number of elements in the set.
Step 4: Calculate 2^4, since n = 4. This equals 16.
Step 5: Understand that the power set includes all possible subsets of B, including the empty set and the set itself.
Step 6: List all the subsets: {}, {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}.
Step 7: Confirm that there are 16 subsets listed, which matches the calculation from Step 4.

Power Set – The power set of a set is the set of all possible subsets, including the empty set and the set itself.
Exponential Growth of Subsets – The number of subsets of a set grows exponentially with the number of elements, specifically 2^n for a set with n elements.