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 October 29th, 2012, 03:16 PM #1 Senior Member   Joined: Jul 2012 Posts: 225 Thanks: 0 Discrete Mathematics - logic Hi, another basic question here regarding logic, but one a bit harder to explain. I am asked to prove that the group {¬,->} (IE the operators NOT and implication) form a whole group of operators. That any logic phrase can be written down with these 2 operators. If i understood the question correctly :P The exact words are "prove that {¬,->} form a whole group of operators" Anyone has any idea what this means or how to solve it?
 October 29th, 2012, 04:03 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Discrete Mathematics - logic One way would be to build the 16 binary operations from those two. Easier would be to reduce to a set of known complete operators, if you know such a set.
 October 29th, 2012, 04:44 PM #3 Member   Joined: Oct 2012 Posts: 45 Thanks: 0 Re: Discrete Mathematics - logic Yes. a v b <-> !a->b a ^ b <-> !(a->!b) Any n-ary operator +:{0,1}^n->{0,1} can be written using just {!,v,^} by "translating" its truth table.

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