Discrete Mathematics Interactive Lab

Rules of Inference, Built One Move at a Time

Learn the eight core propositional-logic inference rules progressively, see how each rule transforms premises into conclusions, and practice arranging a complete proof.

Progressive rule discovery Concrete classroom examples Guided proof practice

Start with rules Open proof practice

Progressive Reveal

All eight rules of inference

Each rule is a reusable proof move. A valid argument is one where the truth of all premises guarantees the truth of the conclusion.

1 of 8 rules unlocked

Concrete Examples

Problem solving with rule patterns

The goal is not to memorize names alone. A student should learn to translate, spot the template, and cite the exact rule used.

Full Proof Walkthrough

The checkbook problem, step by step

The solution first removes the office possibility, then uses the remaining breakfast possibility to locate the checkbook.

Original Statements

1
I was looking at the phone bill for payment at breakfast or in my office.
2
If I was looking at the phone bill at breakfast, then the checkbook is on the breakfast table.
3
If I was looking at the phone bill in my office, then the checkbook is on my office table.
4
I did not pay my phone bill.
5
If my checkbook is on my office table, then I paid my phone bill.

Symbol Map

Breakfast lookup

Office lookup

Checkbook on breakfast table

Checkbook on office table

Phone bill paid

Breakfast trail

p → r

Office trail

q → s → t

Unpaid bill

¬t

Final location

r

Symbolic Hypotheses

1
p ∨ q
2
p → r
3
q → s
4
¬t
5
s → t

Conclusion will appear after the final step.