Question

If A = {1, 2, 3, 4}, write down P(A) [the power set of A] by

listing its elements. What is the value of |P(A)|?

Answer 1

The power set P(A) of A = {1, 2, 3, 4} includes all possible subsets of A, totaling 16 subsets. The cardinality |P(A)| equals 16.

Step-by-step explanation:

If A = {1, 2, 3, 4}, the power set of A, denoted as P(A), is the set of all subsets of A, including the empty set and A itself. The power set is:

• {} (also denoted as ∅)
• {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}

The value of |P(A)|, which represents the cardinality (or the number of elements) of the power set of A, is 2^4 = 16, since A has 4 elements and the power set of a set with n elements has 2^n elements.