SOURCE-GROUNDED · DEMONSTRATION SAMPLE
What you’ll learn
Identify propositions, evaluate basic logical connectives, and explain when an implication is false.
Objectives are authored for this sample lesson. They are not instructor-verified learning outcomes.
Start with statements that can be true or false
A proposition is a declarative statement with exactly one truth value: true or false. “The lab is open” is a proposition. “Open the lab” is a command, so it is not a proposition.
↗ Sample · Week 3 transcript · §3.1The basic connectives
Reverses the truth value of p.
True only when both p and q are true.
True when at least one of p or q is true.
False only when p is true and q is false.
Worked example: a promise of feedback
Let p mean “I submit the assignment” and q mean “I receive feedback.” The statement p → q says: if I submit, then I receive feedback.
If I submit but do not receive feedback, p is true and q is false. That is the only case in which the conditional is false.
Truth table · p → q
| p | q | p → q |
|---|---|---|
| True | True | True |
| True | False | False |
| False | True | True |
| False | False | True |
Common mistakes
Don’t confuse an implication with a conjunction.p → q does not require both p and q to be true. When p is false, the implication is true regardless of q.
Negate both parts — and switch the connective.
The negation of p ∨ q is ¬p ∧ ¬q, not ¬p ∨ ¬q. This is De Morgan’s law.
↗ Sample · Week 3 transcript · §3.4Recap
A proposition has one truth value. Conjunction needs both statements to be true; inclusive disjunction needs at least one. An implication fails only in the true → false case.
For De Morgan’s law, negate each statement and switch ∨ with ∧.
Test your understanding
If p is false and q is true, is p → q true or false? Explain your reasoning before opening the five-question check.
Practice accuracy is separate from lesson completion.
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