Subsets

proofs

Published

October 11, 2026

To do

Read §1.3 Subsets
§1.3 exercises: all odd 1–15, plus ★8, ★10
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 (Subset (podmnožina)) Your words.

Theorem 1 (\emptyset \subseteq A for every set A) Your words.

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

Theorem 2 (A set with n elements has 2^n subsets) Your words.

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

Intuition

Your words.

Exercises

★ 8. List all subsets of \{\{0, 1\}, \{0, 1, \{2\}\}, \{0\}\}.

Solution

Your words.

★ 10. List \{X \subseteq \mathbb{N} : \lvert X \rvert \le 1\}.

Solution

Your words.