previous up next
Go backward to Proof
Go up to Top
Go forward to Tuples
RISC-Linz logo

Equality Reasoning

forall A, B, C: (B union A) intersection (C union A) = (B intersection C) union A.
Venn diagram:
We prove the proposition as follows:
(B union A) intersection (C union A) = (commutativity)
(A union B) intersection (A union C) = (distributivity)
A union (B intersection C) = (commutativity)
(B intersection C) union A.

Author: Wolfgang Schreiner
Last Modification: October 14, 1999

previous up next