Discrete maths:- Predicate logic

Question

Consider $F(P), Q(P), L(P)$ denotes statements “Printer $P$ is out of service”, “Print job $P$ is queued” and “Print job $P$ is lost” respectively. Then statement “If a job is queued and lost then some printer are out of service” is represented by

• A. $\exists j (Q(j) \wedge L(j)) \rightarrow \forall p F(P)$
• B. $\exists j (Q(j) \vee L(j)) \rightarrow \exists p F(P)$
• C. $\exists j (Q(j) \wedge L(j)) \rightarrow \exists p F(P)$
• D. $\forall j (Q(j) \wedge L(j)) \rightarrow \exists p F(P)$

Comments

option (C)

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no.i did the same but it is not correct

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I am getting B as answer? @rahul

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c is ans?

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c is the given answer.

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D is wrong because it says that if  for all jobs J they must be in queue and lost then some printer is out of service.

while option c is if some job J is in queue and lost then some printer is out of service.

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I think a job j either queued or lost it can`t be both at the same time which is reflected by option C. thatswhy  i choose B it seems logical to me.

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in that case ist part will be always true because either a job is queued or  it is lost.(covering all possibilities ).

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Satisfying logically  (although it may not be required)

it may be the case that some jobs are in queue and they are not processed (lost) because of the reason that printer is out of service.

 i think it is not that special type of ques( ornaments are made of gold and silver)

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c is correct.I checked in rossen.Its a exercise problem. 1.3(39.c) Indian edition.

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i think the same

Answer 1

sir one request to you please do not post test series question , because of you , when we get same question in test series we skip to solve that particular question and save our time 

sorry to say you sir but its request from gate overflow family 

Comments

I am not sir.just a gate aspirants like you.I used to tag my questions if these are from test series,but i have not tagged some of my latest questions.I will take care next time.If you find such a tag in heading ,you can skip that question.

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It's ohk bro

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you should not solve those questions that have heading as test series . dnt ask him not to post since this help many people for clearing doubt....... gate overflow family needs these discussions

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You can never understand what  my intention ..

And one request read the blogs of Arjun sir .

For go_fam

Answer 2

Answer would be $C$.

A Job is Queued and lost = $\exists_j(Q(j) \wedge L(j))$

Some Printer are Out of service = $\exists_p(F(p))$

Hence, If "A Job is Queued and lost" then "Some Printer are Out of service" =  $\exists_j(Q(j) \wedge L(j))$ $\rightarrow$  $\exists_p(F(p))$