Lesson Notes By Weeks and Term v4 - SHS 3
PROPORTIONAL REASONING
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
PROPORTIONAL REASONING
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: SHS 3
Term: 1st Term
Week: 8
Grade code: 3.1.2.LI.3
Strand code: 1
Sub-strand code: 2
Content standard code: 3.1.2.CS.2
Indicator code: 3.1.2.LI.3
Theme: NUMBERS FOR EVERYDAY LIFE
Subtheme: PROPORTIONAL REASONING
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Logical reasoning is the backbone of clear thinking and problem-solving. It is not just for mathematicians; it is a skill we use every day. When a doctor in Korle Bu diagnoses a patient based on symptoms, when a lawyer in court builds a case, or when a programmer at a tech hub in Accra writes code, they are all using logical reasoning. This lesson introduces the fundamental language and tools of logic, helping us to analyse situations, make sound arguments, and draw valid conclusions from the world around us. We will learn how to break down complex ideas into simple, true-or-false statements and connect them in a structured way.
2.1. Statement and Truth Value
A statement (often represented by letters like `p`, `q`, `r`) is a declarative sentence that can be definitively classified as either True (T) or False (F), but not both. The classification (T or F) is called its truth value. Examples of Statements: `p`: "The capital of Ghana is Accra." (Truth Value: T) `q`: "The river Pra is in the Ashanti Region." (Truth Value: F - It flows through Ashanti, Eastern, Central, and Western regions, forming borders.) `r`: "5 is a prime number." (Truth Value: T) Examples of Non-Statements: "Come here!" (This is a command, not a statement.) "What is your name?" (This is a question.) "Mathematics is interesting." (This is an opinion; its truth value depends on the individual.) 2.2. Logical Connectives
We can combine or modify simple statements using logical connectives.
a) Negation (~): "NOT" The negation of a statement `p`, written as `~p` (read as "not p"), is the statement that is true when `p` is false, and false when `p` is true. Example: `p`: "It is raining today." `~p`: "It is not raining today." Truth Table for Negation: | `p` | `~p` | |:---:|:----:| | T | F | | F | T |