Logic: Propositions, Truth Tables and Sound Arguments

Which of these can be judged true or false right now? 'Close the door.' 'Manila is the capital of Japan.' 'x + 1 = 5.' 'It is raining.'

Learners sort twelve sentence cards (commands, questions, opinions, facts, open sentences, compound statements) into 'can be true/false' and 'cannot', and write their rule.

Groups take the 'can be true/false' pile and split each sentence into its smallest true/false parts, circling the joining words.

• "How many separate claims are in this sentence?"
• "What word joins them?"

Define a proposition as a declarative sentence that is either true or false but not both. Simple propositions have one claim; compound propositions join simple ones with connectives (not, and, or, if…then, if and only if). Introduce symbols p, q, r and the connective symbols.

Pairs rewrite three school rules or a suspension announcement in symbols after defining their simple propositions, e.g. 'If the signal is No. 2 or higher, then classes in SHS are suspended.'

For five sentences, mark P (proposition) or N, and for each proposition mark S (simple) or C (compound) and name the connective.

Accommodation: Filipino translations of the sentences available.

Copy five sentences from a product label, a news item or a conversation. Classify each as proposition or not, simple or compound, and write any compound one in symbols.

Enrolment rule: 'Bring your Form 137 or your birth certificate.' A learner brings both. Is the rule satisfied?

Pairs list every combination of 'has Form 137' and 'has birth certificate' and decide for each whether the rule is satisfied.

Groups fill truth tables for ¬p, p ∧ q and p ∨ q from the four cases, using situations (the enrolment rule for 'or'; 'passed the exam and submitted the project' for 'and').

Consolidate the three basic operations and the inclusive 'or'. Show that a compound proposition's truth value depends only on the truth values of its parts.

Pairs enter TRUE/FALSE combinations in columns A and B, then formulas =NOT(A2), =AND(A2,B2), =OR(A2,B2), and a longer expression such as =AND(A2,NOT(B2)). They predict each row before pressing Enter and investigate any mismatch.

Complete the truth table for ¬p ∨ q and state in which single case it is false.

Accommodation: partially filled table with the p and q columns given.

Write a scholarship rule with two conditions joined by 'and' or 'or'. Build its truth table in Sheets and describe who qualifies.

Your teacher promises: 'If you score 90 or above, I will give you a sticker.' You score 85 and get no sticker. Was the promise broken? You score 85 and still get a sticker?

Pairs decide, for all four cases, whether the promise was broken. The only broken case defines the false row of p → q.

Groups take 'If it rains (p), classes are suspended (q)' and write the sentence with p and q swapped, with both negated, and with both swapped and negated. For each they find a real situation that makes the original true but the new sentence false, if possible.

Formalise the four forms and the biconditional. Build the truth tables side by side to show p → q ≡ ¬q → ¬p and q → p ≡ ¬p → ¬q.

Student A: 'If a number is divisible by 4, it is even. So if a number is even, it is divisible by 4.' Student B: 'If a number is not even, it is not divisible by 4.' Who reasons correctly? Prove it with a counterexample or a truth table.

Given 'If a learner is in Grade 11, then the learner takes General Mathematics', write the converse, inverse and contrapositive and circle the one equivalent to the original.

Accommodation: sentence frames for each form.

Find an advertisement that implies 'If you use this product, you will be successful.' Write its converse and contrapositive and explain which one the ad wants you to believe.

'Either classes are suspended or they are not.' 'It is raining and it is not raining.' One of these is always true and one is never true, whatever the weather. Why?

Groups build truth tables for p ∨ ¬p, p ∧ ¬p, (p → q) ∧ p → q, and (p → q) ∧ q → p, then sort them by whether the final column is all T, all F or mixed.

Define the three classes. Show that modus ponens is a tautology (valid) while affirming the consequent is contingent (invalid). Then evaluate a compound proposition in a described situation by assigning truth values to its parts.

Each group receives a short real-world argument (a suspension announcement chain, a scholarship decision, a social-media claim). They symbolise it, build the truth table in Sheets, classify the form, determine the truth value in the given situation, and present a two-minute verdict.

The class acts as a review panel using the rubric. Groups defend their symbolisation and verdict.

The argument analysis is scored with the rubric. Exit question: given p true and q false, find the truth value of (p ∨ q) → (p ∧ q).

Find one claim online that uses 'if…then' reasoning. Symbolise it, identify the argument form, and write whether it is valid, with a one-sentence reason.