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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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Suppose you need to come up with a password that uses only the letters A, B, and C and which must use each letter at least once. How many such passwords of length 8 are there? ... 3 *3*3*3*3i am getting 3^6*2 where i am wrong(what i miss)
#4
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Suppose there are three types of people in the world.A person is honest if the person always speaks the truth. A person is a liar if the person ... , deduce with appropriate justifications who among A, B and C has committed the crime.
#5
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When three professors are seated in a restaurant, the hostess asks them: Does everyone want coffee? The first professor says: I do not know. The second ... to the professors who want it. How did she figure out who wanted coffee?
#6
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Consider the poset ({3,5,9,15,24,45},|). Which of the following is correct for the given poset? A. There exists a least element but not a ... element and a least elementD. There does not exist a greatest element and a least element
#7
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Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly independent columns of B.
#8
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how to check the validity of an a argument using laws of logics
#9
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A non empty set A is termed as an algebraic structure ________a)with respect to binary operation *b)with respect to ternary operation ?c)with respect to binary operation +d)with respect to unary operation –
#10
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A data file of 1,000,000 records must be stored using bucket hashing. Record length is 350 bytes, the net capacity of a block is 2000 bytes. Keys occupy 32 ... store the whole structure (i.e. data file + hash table) on disc?Select one:
#11
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A hash function h maps 16-bit inputs to 8-bit hash values. What is the largest k such that in any set of 1000 inputs, there are at least k inputs that h maps to the same hash value?
#12
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Your mother-in-law buys 1000 small gifts to give to relatives for Christmas. Each of the 1000 things in different. There are 25 relatives to give gifts to ... question but please trust me many people like me are confused with this doubt.
#13
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2 answers
6 votes
Which of the following compound propositions is/are a tautology?$[p \land (p \rightarrow q)] \rightarrow q$ ...
#14
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Which of the following is the negation of x is even iff x is divisible by 2a) (x is even or x is not divisible by 2) and (x is not even or x is divisible by 2) ... x is not even iff x is not divisible by 2d) x is even if x is divisible by 2
#15
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Let's take a compound propositionsEither it is below freezing or it is snowing.Now if$p$: it is below freezing $q$: it is snowingWill it be $p \vee q$ ... if you are ill you can't appear for example and you must be in one state.
#17
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#18
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#19
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Let $x$ and $y$ be two propositions. Which of the following statements is a tautology /are tautologies?$(\neg x \wedge y) \Rightarrow(y \Rightarrow x)$( ... (\neg x \Rightarrow y)$(x \wedge \neg y) \Rightarrow(y \Rightarrow x)$
#20
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Let $p$ and $q$ be the following propositions:$p$ : Fail grade can be given.$q$ : Student scores more than $50 \%$ marks.Consider the statement: "Fail ... $q \rightarrow p$ $p \rightarrow q$ $\neg p \rightarrow q$