Question

Implement the following Racket functions: (You must use recursion, and not iteration. You may not use side-effects (e.g. set!). )

1. Reflexive? Input: a list of pairs, L and a list S. Interpreting Las a binary relation over the set S, Reflexive? returns #t if L is a reflexive relation over the set S and #f otherwise. Examples: (display "Reflexive?\n") (Reflexive? '((a a) ( bb) (cc)) '(a b c)) ---> #t (Reflexive? '((a a) (bb)) '(a b c)) ---> #f (Reflexive? '((a a) (a s) (bb) (cc)) '(a b c)) ---> #f (Reflexive? '0 '()) ---> #t

Answer 1

#lang racket
;function to check reflexive relation between a set and it's relation
(define (Reflexive? L S)
(cond
;if the two lists are empty return true
((and (empty? L) (empty? S)) #t)
;if only one list is empty return false
((and (empty? L) (not (empty? S))) #f)
((and (not (empty? L)) (empty? S)) #f)
;check the element of the list S and pair in the L
; if they are equal call the function with rest of the lists
;otherwise return false
(else (if (and (eq? (first S) (first (first L))) (eq? (first S) (second (first L)))) (Reflexive? (rest L) (rest S)) #f))
)
)
;test the function
(Reflexive? '((a a) (b b) (c c)) '(a b c))
(Reflexive? '((a a) (b b)) '(a b c))
(Reflexive? '((a a) (a s) (b b) (c c)) '(a b c))
(Reflexive? '() '())

2 EN Activities DrRacket - Thu 07:20 Untitled - DrRacket* File Edit View Language Racket Insert Tabs Help Untitled (define .... Check Syntax Debug | Macro Stepper # Run Stop #lang racket ; function to check reflexive relation between a set and it's relation (define (Reflexive? LS) (cond ;if the two lists are empty return true ((and (empty? L) (empty? S)) #t) ;if only one list is empty return false ((and (empty? L) (not (empty? S))) #f) ((and (not (empty? L)) (empty? S)) #f) ; check the element of the list S and pair in the L ; if they are equal call the function with rest of the lists ; otherwise return false (else (if (and (eq? (first S) (first (first L))) (eq? (first s) (second (first L)))) (Reflexive? (rest L) (rest S)) #f)) ;test the function (Reflexive? '((a a) (bb) (cc) '(a b c)) (Reflexive? '((a a) (bb) (a b c)) (Reflexive? '((a a) (as) (bb) (cc)) '(a bc)) (Reflexive? '()'() a Welcome to DrRacket, version 6.11 (3m). Language: racket, with debugging; memory limit: 256 MB. #t #f #f #t Determine language from source 16:18 349.44 MB

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