help with discrete math hw •.. and one extra: relational composition which generalizes composition of functionsa (RoS) c ::= 3b E B. (a S b) ^ (b R c).In other words, a is related to c in RoS if starting at a you can follow an S arrow to the startof an R arrow and then follow the R arrow to get to c.Here is one worked example to get you started:- Search description: The set of pages containing the word "logic"- Solution expression: M'("logic")Find similar solutions for each of the following searches:(a) The set of pages containing the word “set" and the word “theory"(b) The set of pages containing the words “set" and "theory" that have been recommendedby "Wiggins"(c) The set of endorsers who have recommended pages containing the words “discrete" and"mathematics"(d) The relation that relates endorser e and word w iff e has recommended a page containing(e) The set of pages that have at least one incoming or outgoing link(f) The relation that relates word w and page p iff w appears on a page that links to p(g) The relation that relates word w and endorser e iff w appears on a page that links to apage that e recommends(h) The relation that relates pages pį and p2 iff p2 can be reached from pį by following asequence of exactly 4 links The language of sets and relations may seem remote from the practical world of programming,but in fact there is a close connection to relational databases, a very popular software applicationbuilding block implemented by such software packages as MYSQL. This problem explores theconnection by considering how to manipulate and analyze a large data set using operators oversets and relations. Systems like MySQL are able to execute very similar high-level instructionsefficiently on standard computer hardware, which helps programmers focus on high-level design.Consider a basic Web search engine, which stores information on Web pages and processes queriesto find pages satisfying conditions provided by users. At a high level, we can formalize the keyinformation as:• A set P of pages that the search engine knows aboutA binary relation L (for link) over pages, defined such that pı L p2 iff page pi links to p2• A set E of endorsers, people who have recorded their opinions about which pages arehigh-quality• A binary relation R (for recommends) between endorsers and pages, such that e R p iff persone has recommended page pA set W of words that may appear on pages• A binary relation M (for mentions) between pages and words, where p M w iff word w appearson page pEach part of this problem describes an intuitive, informal query over the data, and your job is toproduce a single expression using the standard set and relation operators, such that the expressioncan be interpreted as answering the query correctly, for any data set. Your answers should use onlythe set and relation symbols given above, in addition to terms standing for constant elements of Eor W , plus the following operators introduced in the text:set union U.• set intersection n.set difference –.• relation image-for example, R(A) for some set A, or R(a) for some specific element a.• relation inverse '.

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help with discrete math hw •.. and one extra: relational composition which generalizes composition of functionsa (RoS) c ::= 3b E B. (a S b) ^ (b R c).In other words, a is related to c in RoS if starting at a you can follow an S arrow to the startof an R arrow and then follow the R arrow to get to c.Here is one worked example to get you started:- Search description: The set of pages containing the word &#34;logic&#34;- Solution expression: M'(&#34;logic&#34;)Find similar solutions for each of the following searches:(a) The set of pages containing the word “set&#34; and the word “theory&#34;(b) The set of pages containing the words “set&#34; and &#34;theory&#34; that have been recommendedby &#34;Wiggins&#34;(c) The set of endorsers who have recommended pages containing the words “discrete&#34; and&#34;mathematics&#34;(d) The relation that relates endorser e and word w iff e has recommended a page containing(e) The set of pages that have at least one incoming or outgoing link(f) The relation that relates word w and page p iff w appears on a page that links to p(g) The relation that relates word w and endorser e iff w appears on a page that links to apage that e recommends(h) The relation that relates pages pį and p2 iff p2 can be reached from pį by following asequence of exactly 4 links The language of sets and relations may seem remote from the practical world of programming,but in fact there is a close connection to relational databases, a very popular software applicationbuilding block implemented by such software packages as MYSQL. This problem explores theconnection by considering how to manipulate and analyze a large data set using operators oversets and relations. Systems like MySQL are able to execute very similar high-level instructionsefficiently on standard computer hardware, which helps programmers focus on high-level design.Consider a basic Web search engine, which stores information on Web pages and processes queriesto find pages satisfying conditions provided by users. At a high level, we can formalize the keyinformation as:• A set P of pages that the search engine knows aboutA binary relation L (for link) over pages, defined such that pı L p2 iff page pi links to p2• A set E of endorsers, people who have recorded their opinions about which pages arehigh-quality• A binary relation R (for recommends) between endorsers and pages, such that e R p iff persone has recommended page pA set W of words that may appear on pages• A binary relation M (for mentions) between pages and words, where p M w iff word w appearson page pEach part of this problem describes an intuitive, informal query over the data, and your job is toproduce a single expression using the standard set and relation operators, such that the expressioncan be interpreted as answering the query correctly, for any data set. Your answers should use onlythe set and relation symbols given above, in addition to terms standing for constant elements of Eor W , plus the following operators introduced in the text:set union U.• set intersection n.set difference –.• relation image-for example, R(A) for some set A, or R(a) for some specific element a.• relation inverse '.

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