---

Tautology

Define

A statement that is always ‘true’.

Explore

Compute whether a given molecular statement is a tautology.

• ‘scheme/tautology?’

  Search truth tables for the absence of ‘FALSE’ to identify tautologies.

  Builds on ‘scheme/truth-table’.

  <<scheme/truth-table>>
  
  (define (tautology? procedure arity)
    (not (member #f (map (lambda (row)
                           (car (reverse row)))
                         (truth-table procedure arity)))))
  

  <<scheme/tautology?>>
  
  (unless (tautology? (lambda (p) (or p #t)) 1) (raise #f))
  (unless (tautology? (lambda (p q) (or p q #t)) 2) (raise #f))
  (unless (tautology? (lambda (p q r) (or p q r #t)) 3) (raise #f))
  
  (when (tautology? (lambda (p) (or p)) 1) (raise #f))
  (when (tautology? (lambda (p q) (or p q)) 2) (raise #f))
  (when (tautology? (lambda (p q r) (or p q r)) 3) (raise #f))
  
  "tests passed"
  

  tests passed