Proof

(related to Proposition: Associativity of Disjunction)

$[[x]]_I$ $[[y]]_I$ $[[z]]_I$ $[[x \vee y]]_I$ $[[y \vee z]]_I$ $[[(x \vee y)\vee z]]_I$ $[[x\vee (y \vee z)]]_I$
$1$ $1$ $1$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $1$ $1$ $1$
$1$ $0$ $1$ $1$ $1$ $1$ $1$
$0$ $0$ $1$ $0$ $1$ $1$ $1$
$1$ $1$ $0$ $1$ $1$ $1$ $1$
$0$ $1$ $0$ $1$ $1$ $1$ $1$
$1$ $0$ $0$ $1$ $0$ $1$ $1$
$0$ $0$ $0$ $0$ $0$ $0$ $0$

Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs


References

Bibliography

  1. Mendelson Elliott: "Theory and Problems of Boolean Algebra and Switching Circuits", McGraw-Hill Book Company, 1982