Cartesian product

proofs

Published

October 11, 2026

To do

Read §1.2 The Cartesian product
§1.2 exercises: all odd 1–19, plus ★7, ★8
Paper: all listed exercises. Odd ones have solutions at the back. Mark ✓ / ✗ / S.
Notebook: write each div below in your own words. Copy the ★ exercises in clean.

Definition 1 (Ordered pair (uspořádaná dvojice)) Your words.

Definition 2 (Cartesian product (kartézský součin)) Your words.

Theorem 1 (Cardinality of A \times B) Your words.

Proof. Cover the book’s proof. Try 10–15 min first.

Intuition

Your words.

Exercises

★ 7. List \{\emptyset\} \times \{0, \emptyset\} \times \{0, 1\}.

Solution

Your words.

★ 8. List \{0, 1\}^4.

Solution

Your words.