**
**
**(****First
step: "x[Dx®x
is an undergraduate who worked harder than John] and $x[x is an undergraduate who worked harder
than John Ù Dx] and $x[x is an undergraduate who worked harder
than John Ù ¬Dx]**
**Next
step: [["x[Dx®[UxÙHxa]]Ù$x[[UxÙHxa]ÙDx]]Ù$x[[UxÙHxa]Ù¬Dx]]**
**(Or:
[[¬$x[DxÙ¬[UxÙHxa]]Ù$x[[UxÙHxa]ÙDx]]Ù$x[[UxÙHxa]Ù¬Dx]])**
**Notice
that, because none of the occurrences of "$x" were within the scope of any other
quantifier containing "x" we could stick to the same variable
throughout.** |