Lesson Notes By Weeks and Term v4 - SHS 3
PROPORTIONAL REASONING
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PROPORTIONAL REASONING
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Subject: Mathematics
Class: SHS 3
Term: 1st Term
Week: 2
Grade code: 3.1.2.LI.2
Strand code: 1
Sub-strand code: 2
Content standard code: 3.1.2.CS.1
Indicator code: 3.1.2.LI.2
Theme: NUMBERS FOR EVERYDAY LIFE
Subtheme: PROPORTIONAL REASONING
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In our daily lives, we constantly make decisions based on information. We listen to news reports, read agreements, and follow instructions. Logical reasoning is the tool that helps us understand the structure of these statements and determine whether they are true or false. This skill is crucial not just for passing examinations, but for becoming critical thinkers who can make informed judgments in our community, in business, and in our personal lives. For instance, when a mobile money agent gives you terms like "You must provide your ID card *and* state your full name," understanding the logic of "and" is essential.
Teacher's Note: This topic is about reasoning and structure. Encourage learners to think carefully about the meaning of words. Use a collaborative approach, asking students for examples throughout the explanation. A. What is a Statement? In logic, a statement (or proposition) is a declarative sentence that is either True (T) or False (F), but not both. The truthfulness or falsity of a statement is called its truth value. Examples of Statements: "Accra is the capital city of Ghana." (This is a True statement. Its truth value is T). "The River Volta is in the Ashanti Region." (This is a False statement. Its truth value is F). "5 + 7 = 12." (This is a True statement. Its truth value is T). "2 is an odd number." (This is a False statement. Its truth value is F). Examples of sentences that are NOT statements: "What is your name?" (This is a question). "Stop making noise!" (This is a command). "Mathematics is interesting." (This is an opinion; it is not objectively true or false for everyone). "x + 3 = 5." (This is an open sentence. Its truth value depends on the value of x). B. Simple and Compound Statements Simple Statement: A statement that contains a single idea or piece of information. Example: "Kojo is a student." (Let's call this statement *p*). Compound Statement: A statement formed by joining two or more simple statements with words called logical connectives. Example: "Kojo is a student, and he plays football." This is made of two simple statements: p: "Kojo is a student." q: "He plays football." C. Logical Connectives: Conjunction and Disjunction
We will focus on two main connectives today. Conjunction ("and" / "but") The conjunction joins two statements with the word "and". The symbol for conjunction is ∧. A compound statement `p ∧ q` (read as "p and q") is TRUE only if BOTH p and q are true. If either p or q (or both) is false, the entire compound statement is false. The word "but" often acts logically like "and". It adds a sense of contrast but the logical requirement is the same. For example, "Abu is a farmer *but* not a brother" is a conjunction.