Cardinality of a Finite Set Worksheet with Answer Key

What's on the worksheet

1. Find the cardinality of each set, counting each distinct element once.
   the set of digits used in writing 2^{16} = 65{,}536\{4, -4, \lvert -4\rvert, 2^2, -2^2, 16\}\{x^2 - 4x : x \in \{0, 1, 2, 3, 4, 5\}\}\{\{1, 2\}, \{2, 1\}, \{1\}, \varnothing\}\{\varnothing, \{\varnothing\}, \{\varnothing, \varnothing\}\}
2. Word problem: raffle tickets numbered 135 to 892 that win a prize.
3. Find the cardinality of each set of integers defined by an inequality.
   \{x \in \mathbb{Z} : -7 < 2x + 3 \le 15\}\{x \in \mathbb{Z} : 10 < x^2 < 70\}\{x \in \mathbb{Z} : x^2 < 6x\}\{x \in \mathbb{Z} : 2x + 1 = 8\}
4. Give a one-to-one match for each set and state its cardinality.
5. Find the sizes of two sets and explain how they compare.
6. Count four-digit palindromes and compare with another set.