Q.If $A = \{1, 2, 3, 4\}$, write the power set $P(A)$ and verify that $n(P(A)) = 2^4$.

[!TLDR] List all $2^4 = 16$ subsets of a 4-element set. [!ANSWER] $P(A)$ has all 16 subsets of …

$A = \{1,2,3,4\}$ has $n(A) = 4$ elements. Listing every subset by size: size 0: $\varnothing$; size 1: $\{1\},\{2\},\{3\},\{4\}$; size 2: $\{1,2\},\{1,3\},\{1,4\},\{2,3\},\{2,4\},\{3,4\}$; size 3: $\{1,2,3\},\{1,2,4\},\{1,3,4\},\{2,3,4\}$; size 4: $\{1,2,3,4\}$. Counting: $1 + 4 + 6 + 4 + 1 = 16$ subsets in total, matching $2^4 = 16$. [!ANSWER] $P(A) = {\varno …

List subsets systematically by size (0 through 4 elements) so none are missed or repea …

A common slip is forgetting to include $\varnothing$ or $A$ itself as su …