This document contains detailed notes from Lecture 20 of the CO2412 course on Computational Thinking, focusing on exam revision topics including propositional logic and statistical measures. The lecture covers essential concepts such as the validity of arguments, logical equivalence, and key measur...
CO2412: Computational Thinking
Lecture 20 – Exam Revision 03
Propositional Logic
1. Definition and Purpose
o Propositional Logic is used to establish the validity of arguments,
providing rules that allow us to judge whether an argument is sound
or unsound. This helps determine whether a conclusion drawn from
stated premises is valid.
2. Propositions
o A proposition is a statement that is either true or false.
o Examples:
6 < 24 (True)
3 + 2 = 4 (False)
"Tomorrow is my birthday" (Context-dependent truth value)
3. Non-Propositional Statements
o Statements like questions and exclamations are not propositions as
they do not equate to true or false.
o Examples:
"Keep off the grass!" (Exclamation)
"What time is it?" (Question)
Compound Propositions and Connectives
1. Negation
o The negation of a proposition reverses its truth value. If p is true,
then ¬p (not p) is false, and vice versa.
o Example:
If p = "It is raining," then ¬p = "It is not raining."
, 2. Conjunction (AND)
o The conjunction of two propositions p and q is true only when both p
and q are true.
o Example:
p: The sun is shining.
q: I am learning logic.
p ˄ q: The sun is shining AND I am learning logic.
3. Disjunction (OR)
o The disjunction of two propositions p and q is true if at least one of
them is true.
o Inclusive OR (˅): Either or both propositions can be true.
o Exclusive OR (XOR): Exactly one but not both propositions are
true.
4. Implication (Conditional)
o Implication: p → q (If p, then q). This is false only when p is true,
and q is false.
o Example:
p: I eat breakfast.
q: I don’t eat lunch.
p → q: If I eat breakfast, then I don’t eat lunch.
5. Bi-conditional
o Bi-conditional: p ↔ q (p if and only if q). This is true when both
propositions have the same truth value.
o Example:
p: I eat breakfast.
q: I don’t eat lunch.
p ↔ q: I eat breakfast if and only if I don’t eat lunch.
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