Year 13/A2 Pure Chapter 1.1A (Algebraic Methods)

This video introduces Pure mathematics for Year 13, and we begin by delving into the topic of mathematical proof.
I have opted to split this proof subchapter into 2 parts - 1.1A and 1.1B - owing to the relative complexity of the topic and the large variety of question types that may be encountered. 1.1A largely recaps Year 12 and lays the groundwork for further proof by contradiction examples in video 1.1B.

Introduction: 0:00

Solution to Warm-Up Q1: 1:13
Solution to Warm-Up Q2: 3:32
Solution to Warm-Up Q3: 6:16
Solution to Warm-Up Q4: 10:36

YEAR 12/AS PROOF RECAP AND WORKED EXAMPLES
Recap of proof types encountered so far: 13:30
PROOF A (By exhaustion): 16:28
PROOF B (By counter-example): 18:15
PROOF C (Deduction/algebraic): 19:24
PROOF D (From a "statement of fact"): 21:05

Subsets of the Real number line: 23:50
Closure under the laws of arithmetic: 25:57

FURTHER PROOFS USING REPRESENTATIVES
Introduction: 28:30
Worked Example 1: 31:26
Worked Example 2: 34:51
Worked Example 3: 37:34

PROOF BY CONTRADICTION
Introduction: 40:48
Negations: 43:27
Common negation structures: 43:46

Worked Example 4: 48:05
Worked Example 5: 51:09