I am just testing how far the built in blogger editor can help in laying out proofs. Please ignore this.

Question: prove distributivity of OR over OR ( I am using "OR" and "AND" for disjunction and conjunction operators , == for equivalence. The reasoning for each step is to the side after a --),

(The calculus used is EQ from "A logical Approach to Discrete Math". This is theorem 3.41, just something chosen at random - but I've used only axioms + theorems proven till that point in the book ) .

prove p OR (q OR r) == (p OR q) OR (p OR r)

p OR (q OR r) -- LHS

== ((p OR q) OR r) -- associativity of Or

== (( p OR q) OR r) OR false -- False is the identity of OR

== (( p OR q) OR r) OR (NOT true) -- definition of false

== (m or r) OR (NOT true) -- substituting m for (p OR q), Leibniz

== m OR (r OR (NOT true)) -- associativity of OR

== m OR ( r OR (NOT (p == p)) ) -- true is identity of ==

== m OR ( r OR ( NOT p == p )) -- distributivity of NOT over ==

== m OR (r OR (NOT p) == r OR p ) -- distributivity of OR over ==

== m OR (r OR p == r OR (NOT p)) -- symmetry of OR

== (m OR r OR p) == (m OR r OR (NOT p)) -- distributivity of OR over ==

==(p OR q OR r OR p)== (m OR r OR (NOT p)) -- replacing m with (p OR q), Leibniz

==(p OR q) OR (r OR p)== (m OR r OR (NOT p)) --associativity of OR

==(p OR q) OR (p OR r)== (m OR r OR (NOT p)) --symmetry of OR

==(p OR q) OR (p OR r)== (m OR (NOT p) OR r) --symmetry of OR

==(p OR q) OR (p OR r)== (p OR q OR (NOT p) OR r) --expanding m to p OR q, Leibniz

==(p OR q) OR (p OR r)== (p OR (NOT p) OR q OR r) --symmetry of OR

==(p OR q) OR (p OR r)== ( true OR q OR r) -- Excluded Middle

== (p OR q) OR (p OR r)== ( true OR r) -- true is the Zero of OR

== (p OR q) OR (p OR r) == true -- true is the Zero of OR

== (p OR q) OR (p OR r) -- true is the Identity of ==

== RHS . QED

Conclusion: What a mess. I need Latex dammit. Anyone know of a *non* wordpress blog with a latex plugin? (I don't want JS rendering, for which there are a few options. I want an image (png, gif, jpeg whatever) generated on the server and plugged in appropriately).

Ravi Mohan's Tech Blog. To read my non technical blog, click here

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## 2 comments:

Use a formula chart

@anonymous.

Interesting. Thanks!

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