1
Statement vs Non-Statement
A statement is a declarative sentence that is either true or false, but not both.
$12 \text{ is a multiple of } 3$ (True statement)
$2x + 5 = 11$ (Open sentence - NOT a statement)
Please close the door! (Command - NOT a statement)
2
Implications & Variations
Given implication: If $p$, then $q$ ($p \implies q$):
Converse (Akas): $q \implies p$
Inverse (Songsangan): $\sim p \implies \sim q$
Contrapositive: $\sim q \implies \sim p$
Contrapositive has the same truth value as implication!
3
Forms of Deductive Arguments
Three valid SPM forms of deduction:
Form I: Premise 1: All A are B. Premise 2: C is A. $\implies$ Conclusion: C is B.
Form II: Premise 1: If $p$, then $q$. Premise 2: $p$ is true. $\implies$ Conclusion: $q$ is true.
Form III: Premise 1: If $p$, then $q$. Premise 2: Not $q$ ($\sim q$). $\implies$ Conclusion: Not $p$ ($\sim p$).
Examiner Secret: Inductive Conclusion vs Deductive Conclusion
Inductive Generalisation (General rule from pattern): Look at the common coefficients and write the formula with $n = 1, 2, 3, \dots$ at the end. Forgetting to write $n = 1, 2, 3, \dots$ loses the final mark!
"If and only if" (jika dan hanya jika): Means the implication holds both ways: Implication 1: "If $p$, then $q$" AND Implication 2: "If $q$, then $p$". Both must be written out completely in SPM!