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diff --git a/assignment1.mdwn b/assignment1.mdwn
index 453fa546..fa02cb83 100644
--- a/assignment1.mdwn
+++ b/assignment1.mdwn
@@ -17,8 +17,8 @@ Booleans
 
 Recall our definitions of true and false.
 
->   **true** defined to be `\t \f. t`  
->   **false** defined to be `\t \f. f`
+>   **true** is defined to be `\t \f. t`  
+>   **false** is defined to be `\t \f. f`
 
 In Racket, these can be defined like this:
 
@@ -40,9 +40,7 @@ evaluates to 10.
 
 <LI>Define an `and` operator.
 
-<LI>Define an `xor` operator. 
-
-If you haven't seen this term before, here's a truth table:
+<LI>Define an `xor` operator. If you haven't seen this term before, here's a truth table:
 
     true xor true = false
     true xor false = true
@@ -75,7 +73,7 @@ Pairs
 
 Recall our definitions of ordered pairs.
 
->   the pair **(**x**,**y**)** is defined as `\f. f x y`
+>   the pair **(**x**,**y**)** is defined to be `\f. f x y`
 
 To extract the first element of a pair p, you write:
 
@@ -93,13 +91,11 @@ Now we can write:
 	(p get-first)   ; will evaluate to 10
 	(p get-second)  ; will evaluate to 20
 
-If you're bothered by having the pair to the left and the function that
+If you're puzzled by having the pair to the left and the function that
 operates on it come second, think about why it's being done this way: the pair
-is a package that takes a function for operating on its elements as an
-argument, and returns the result of operating on its elemens with that
-function. In other words, the pair is also a function.  (Of course, in the
-untyped lambda calculus, absolutely *everything* is a function: functors,
-arguments, abstracts, redexes, values---everything.)
+is a package that takes a function for operating on its elements *as an
+argument*, and returns *the result of* operating on its elements with that
+function. In other words, the pair is a higher-order function. (Consider the similarities between this definition of a pair and a generalized quantifier.)
 
 If you like, you can disguise what's going on like this:
 
@@ -114,19 +110,17 @@ instead of:
 
 	(p get-first)
 
-However, the latter is still what's going on under the hood.
+However, the latter is still what's going on under the hood. (Remark: `(lifted-f ((make-pair 10) 20))` stands to `(((make-pair 10) 20) f)` as `(((make-pair 10) 20) f)` stands to `((f 10) 20)`.)
 
 
 <OL start=13>
-<LI>Define a `swap` function that reverses the elements of a pair.
-
-Expected behavior:
+<LI>Define a `swap` function that reverses the elements of a pair. Expected behavior:
 
 	(define p ((make-pair 10) 20))
 	((p swap) get-first) ; evaluates to 20
 	((p swap) get-second) ; evaluates to 10
 
-Write out the definition of swap in Racket.
+Write out the definition of `swap` in Racket.
 
 
 <LI>Define a `dup` function that duplicates its argument to form a pair