#Propostional logic
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clever tiger
i mean, each element of A is just some function of the variable a
that returns true or false
so can you enumerate all possible statements that follow that
arctic harness
i still dont understand
clever tiger
i still dont understand
the A/R<-> means the set of equivalence classes of A with equivalence relation R<->
aka, it's the sets of sentences, so that any 2 sentences in a particular set, are equivalent to each other
arctic harness
oh so
the sentences need to have an equivalence relation, transitive, reflexive and symmetric
clever tiger
indeed, you can check that R<-> satisfies all of those
arctic harness
it says only using the variable a
clever tiger
like for example a^a is equivalent to a
arctic harness
if we dont use intermediate values then it can only be a ^ a, a V a
that seems to small of a set
clever tiger
if we dont use intermediate values then it can only be a ^ a, a V a
both of which are just a
arctic harness
ye but only 2 sentences form
arctic harness
i mean in the set
clever tiger
those are just 2 elements of A
R is the set of pairs of elements of A that are equivalent to one another
arctic harness
True that
so the equivalence class will also be infinite?
im very new to equivalence stuff
clever tiger
so the equivalence class will also be infinite?
depends what you mean
like
each equivalence class (of which there are 1) has infinitely many elements, i guess you could say that
arctic harness
$[a_{r}] = {x \mid aRx}$
solid tendonBOT
XE
