Racket code only please. No loops or hash use.Allowed functions are:define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. map, append-map, andmap, ormap, filter7. +, -, /, *8. Functions you implement Implement the following Racket functions:1. Reflexive?Input: a lists of pairs, L and the set S over which the relation is defined. Interpreting theinput as a binary relations, return return #T if it is reflexive and #F otherwise.2. Symmetric?Input: a lists of pairs, L. interpreting the input as a binary relation, return return #T if it issymmetric and #F otherwise.

Here is the implementation for the two functions in Racket:

Answered: Implement the following Racket…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Racket code only please. No loops or hash use.

Allowed functions are:

define, let
2. lambda
3. cons, car, cdr, list, list?, append, empty?, length, equal?
4. and, or, not
5. if, cond
6. map, append-map, andmap, ormap, filter
7. +, -, /, *
8. Functions you implement

Implement the following Racket functions:
1. Reflexive?
Input: a lists of pairs, L and the set S over which the relation is defined. Interpreting the
input as a binary relations, return return #T if it is reflexive and #F otherwise.
2. Symmetric?
Input: a lists of pairs, L. interpreting the input as a binary relation, return return #T if it is
symmetric and #F otherwise.

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They are failing for these cases. Do you have any advice? Thank you!

(reflexive? '((a . b) (b . c) (d . e) (a . a) (b . b) (c . c) (d . d) (e . e)) '(a b c d e))

(symmetric? '((a . b) (b . a) (c . d) (d . c) (2 . 1) (1 . 2))) #t "symmetric-2") ;failed

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