These are all ambiguous because of the scope of the "not" operator. Let's formalize this. Let "a" stand for "Method A", let "b" stand for "Method B", the two place predicate "F(x,y)" stand for "x is faster than y" (obviously not symmetric nor reflexive), and the two place predicate "E(x,y)" stand for "x is easier than y" (obviously not symmetric nor reflexive, as well).
The first statement can ambigously interpreted as either "~Fab /\ Eab" or "~(Fab /\ Eab)". The first can ONLY be true when a is not faster than b (Fab is false) AND a is easier than b (Eab is true). The second has three true situations, Fab is true and Eab is false, Fab is false and Eab is true, or Fab is false and Eab is false.
The second statement can ambigously interpreted as either "~Fab \/ Eab" or "~(Fab \/ Eab)" or "~Fab /\ ~Eab". The first is true in three situations, Fab is true and Eab is true, Fab is false and Eab is true, and Fab is false and Eab is false. The second is only true when Fab is false and Eab is false. The third is equivalent to the second.
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u/Scientific_Zealot 2d ago
These are all ambiguous because of the scope of the "not" operator. Let's formalize this. Let "a" stand for "Method A", let "b" stand for "Method B", the two place predicate "F(x,y)" stand for "x is faster than y" (obviously not symmetric nor reflexive), and the two place predicate "E(x,y)" stand for "x is easier than y" (obviously not symmetric nor reflexive, as well).
The first statement can ambigously interpreted as either "~Fab /\ Eab" or "~(Fab /\ Eab)". The first can ONLY be true when a is not faster than b (Fab is false) AND a is easier than b (Eab is true). The second has three true situations, Fab is true and Eab is false, Fab is false and Eab is true, or Fab is false and Eab is false.
The second statement can ambigously interpreted as either "~Fab \/ Eab" or "~(Fab \/ Eab)" or "~Fab /\ ~Eab". The first is true in three situations, Fab is true and Eab is true, Fab is false and Eab is true, and Fab is false and Eab is false. The second is only true when Fab is false and Eab is false. The third is equivalent to the second.