4. (Beta reductions) For each of the following expressions, identify the redexes and, for each redex, do only one beta reduction step to reduce the redex. If renaming is needed you should do renaming first before doing the beta reduction Example 1 Ax x x) Answer Example 2 (Ax. ny. 12. * y Aw. z)(x y z w) Answer ny. Az. * y aw. 2)(x y z w) "(.x. du. Av. x u lw. )(x y z w) (du. iv. x u Aw. v) x y z w) - lu. iv. x y z w) u lw.v Example 3 (Ax. (dy. x)y) 2 Answer // This expression has two redexes. You should show one beta reduction for each redex separately not one // after the other ay x)y) 2-dy. 2) // beta reduction for first redex (Ax. x)) 2 (Ax. x) z // beta reduction for second redex // The examples above clearly show that you should answer by highlighting the redexes and also highlight the result of the // reduction (and the renaming if applicable). You should follow the same format as the examples below 4.1. ((x, 2)(x2)) (ax. (ax. 2)(x2)) 4.2. (ax. (ay. x) (Az.xyz)) (y 2) 4.3. (ax. ly. x Az. xy Ax. xz) ((Azyz) yz) 4.4. iy. (ax. ly. x Ax. 1z.xyz) ((Az. yz) (Azyz)) 4.5. (ay. x Az.xyz) (ay, Az yz)