Problem 2 [6pt] Recall that under Church encoding, we have the following definitions: IF 4 16 t f.bt f TRUE 4 At f. t FALSE 4 At f. f a) (2pt) Fully evaluate (1x. (x Y TRUE)) FALSE so that no further -reduction is possible.. b) (4pt) Define XOR using -calculus and IF TRUE FALSE as defined above. Show that with your definition, XOR FALSE TRUE fully evaluates to TRUE. And that XOR TRUE TRUE fully evaluates to FALSE. Show every step of the evaluation. Problem 2 [6pt] Recall that under Church encoding, we have the following definitions: IF 4 16 t f.bt f TRUE 4 At f. t FALSE 4 At f. f a) (2pt) Fully evaluate (1x. (x Y TRUE)) FALSE so that no further -reduction is possible.. b) (4pt) Define XOR using -calculus and IF TRUE FALSE as defined above. Show that with your definition, XOR FALSE TRUE fully evaluates to TRUE. And that XOR TRUE TRUE fully evaluates to FALSE. Show every step of the evaluation