Proof

(related to Proposition: Associativity of Conjunction)

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

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References

Bibliography

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