What’s on the Proof Techniques poster
A 7-row table: Technique · Assume · Establish.
Proving P ⇒ Q. Pick the shape that fits the hypothesis.
- Direct — P — Q follows
- Contrapositive — ¬Q — ¬P follows
- Contradiction — P and ¬Q — An absurdity
- Induction — P(k) — P(k + 1)
- Exhaustion by cases — Each case in turn — Q in every case
- Counterexample — Nothing — One instance failing
- Construction — Nothing — Build the object
Contrapositive and contradiction are not the same thing. A contrapositive proof is a direct proof of a logically equivalent statement.
Questions about the Proof Techniques poster
- What’s on the Proof Techniques poster?
- A 7-row table: Technique · Assume · Establish. Proving P ⇒ Q. Pick the shape that fits the hypothesis. Direct — P — Q follows; Contrapositive — ¬Q — ¬P follows; Contradiction — P and ¬Q — An absurdity; Induction — P(k) — P(k + 1); Exhaustion by cases — Each case in turn — Q in every case; Counterexample — Nothing — One instance failing; Construction — Nothing — Build the object. Contrapositive and contradiction are not the same thing. A contrapositive proof is a direct proof of a logically equivalent statement.
- Who is the Proof Techniques poster for?
- Proof Techniques belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning discrete mathematics can pin it up — a beginner, a student mid-course, or someone revising years later.
- When should you use the Proof Techniques poster?
- When a proof stalls, the usual fix is a different technique, not more effort. A wall chart earns its place by being glanceable from where the work is happening, so Proof Techniques belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Proof Techniques?
- The Binomial Theorem, Counting Principles and Euler & Hamiltonian Paths sit alongside Proof Techniques in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Binomial TheoremCounting PrinciplesEuler & Hamiltonian Paths
- Is the Proof Techniques poster free to download and print?
- Yes. Proof Techniques downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Proof Techniques poster print at?
- Proof Techniques is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Proof Techniques loses nothing.Printing guide
Related posters
Charts that sit alongside Proof Techniques on the same wall.
Browse every Mathematics poster, or start from the full catalogue.