Commutativity of conjunction
- Commutativity of conjunction
-
In logic, the commutativity of conjunction demonstrates that predicates on both sides of a logical conjunction operator are interchangeable. This logical law is a part of classical logic.[1]
For any propositions H1, H2, ... Hn, and permutation σ(n) of the numbers 1 through n, it is the case that:
- H1
H2 ... Hn
is equivalent to
- Hσ(1) Hσ(2) Hσ(n).
For example, if H1 is
- It is raining
H2 is
- Socrates is mortal
and H3 is
- 2+2=4
then
It is raining and Socrates is mortal and 2+2=4
is equivalent to
Socrates is mortal and 2+2=4 and it is raining
and the other orderings of the predicates.
This law is also known as `and introduction' and is quite commonly abbreviated as `vI'.
References
- ^ Elliott Mendelson (1997). Introduction to Mathematical Logic. CRC Press. ISBN 0412808307.
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