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Syllabus: Propositional and first order logic.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1}&\textbf{2024-2}&\textbf{2023}& \textbf{2022}& \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&0&1&1& 0 & 1&1&0&0.67&1
\\\hline\textbf{2 Marks Count}&0&0&0&0 & 0&0&0&0&0
\\\hline\textbf{Total Marks}& 0&1&1& 0 & 1&1&\bf{0}&\bf{0.67}&\bf{1}\\\hline
\end{array}}}$$

Recent questions in Mathematical Logic

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Which is appropriate for the statement and why?
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I was reading cumulative distribution function from sheldon ross and I had a doubt regarding one of it's properties.The following are properties of the cumulative ... What does this $4^{th}$ property actually mean can anyone explain?
#983
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At a party there are 15 men and 20 women.How many ways are there to form fifteen couples consisting of one man and one woman? is it p(20,15)How many ways ... to form ten couples consisting of one man and one woman?? is it 20C10 * 15C10??
#984
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3. Which of the following are valid?A) (∃!x)(∃!y)J(x,y) <-> (∃!x)(∃!y)J(x,y)B) (∃!x)(∃!y)J(x,y) <-> (∃!y)(∃!x)J(x,y)C) (∃!x)(∃!y)J(x,y) -> (∃!x)(∃!y)J(x,y)D) (∃!x)( ... )(∃!y)J(x,y) -> (∃!x)(∃!y)J(x,y)D) (∃!x)(∃!y)J(x,y) -> (∃!y)(∃!x)J(x,y)
#985
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2. Which of the following are satisfiable?A) (∀x)(∀y)J(x,y) <-> (∀x)(∀y)J(x,y)B) (∀x)(∀y)J(x,y) <-> (∀y)(∀x)J(x,y)C) (∀x)(∀y)J(x,y) -> (∀x)(∀y)J(x,y)D) (∀x)(∀y)J(x,y ... G) (∃x)(∃y)J(x,y) -> (∃x)(∃y)J(x,y)H) (∃x)(∃y)J(x,y) -> (∃y)(∃x)J(x,y)
#986
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1. Which of the following are valid?A) (∀x)(∀y)J(x,y) <-> (∀x)(∀y)J(x,y)B) (∀x)(∀y)J(x,y) <-> (∀y)(∀x)J(x,y)C) (∀x)(∀y)J(x,y) -> (∀x)(∀y)J(x,y)D) (∀x)(∀y)J(x,y) -> ... y)G) (∃x)(∃y)J(x,y) -> (∃x)(∃y)J(x,y)H) (∃x)(∃y)J(x,y) -> (∃y)(∃x)J(x,y)
#987
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#988
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The number of multi sets of size 4 are possible with the elements of the set S={1,2,3,4,5,6} is ?????What does multi set refers to???
#989
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#990
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#991
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Is conjunctive normal form is in gate syllabus????
#992
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Express each of these system specifications using predicates,quantifiers, and logical connectivesb) Whenever there is an active alert, all queued messagesare transmitted. ... don't use implication with ∃x "Which leaves me in confusion.?
#993
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What procedure need to be followed so as to translate english statement to predicate logic for example Every mother loves her children?
#994
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Express each of these system specifications using predicates,quantifiers, and logical connectives.c) The file system cannot be backed up if there is a usercurrently ... If the manual is correct then why two variables x,y are required?
#995
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#996
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Consider the following two statements:S1 : All clear explanations are satisfactory.S2 : Some excuses are unsatisfactory. Which one of the following ... Some excuses are not clear explanations(D)Some explanations are clear excuses.
#997
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#998
744
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can anyone solve the puzzle below:There are some books on the table. If you group them by 3, you get some number of full groups and 2 books remain; if you group ... remain. What is the number of books on the table, if it is less than 100?
#999
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Is the chapter Complex functions part of gate 2019 maths syllabus?Previously questions about analytic functions have been asked a lot. Are they part of the syllabus?
#1000
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Express the statement Every student in this class has studied calculus using predicates andquantifiers.Solution: First, we rewrite the statement so that we can clearly identify ... So, the value is not given as input there. Then why now?