If you have already read and learnt all the examples from this document,
you did wrong! Now you lack exercises to solve by yourself.
You can invent sequents and try to prove that they are valid; the
problem then is that if they are not, you will waste your time trying
to prove their validity in vain. So you must think only of valid sequents,
and then prove them correctly.
Some methods I know to do that are:
- If and are the same formula, but written in some different
ways, then try proving or .
- Take a truth and prove it. For instance:
- Take a lie, negate it, and try to prove that formula. Example:
This method will make you practise reduction to the absurd.
- Convert some formula to its conjunctive normal form (so it
is expressed like something something ...
something). Then you have several formulas which are all
true at the same time: each of the conjunctands. You can select one
of them and assert that when the original formula is true, then that
conjunctand also is.
- Take several formulas at random, and suppose that all of them are
true simultaneously. To do that, write their conjunction (one
other other ...).
This big formula can be modified with the above methods to find some
of its consequences. All this will be useful to practise natural deduction
with several true formulas at the left part of the sequent.
Daniel Clemente Laboreo