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Syllabus: Propositional and first order logic.

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

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Hot questions in Mathematical Logic

2 votes
1 answer
586
Hamiltonian Graph
A complement of a cyclic graph on 5 vertices , has an Hamiltonian circuit . (True/False)
A complement of a cyclic graph on 5 vertices , has an Hamiltonian circuit . (True/False)
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2 votes
2 answers
590
Logically Equivalent justify your answer
1. (∀x (p(x) → q(x)) and (∀x p(x) → ∀x q(x)) 2.∃x p(x)∧∃x q(x) and ∃x (p(x)∧q(x)) 3.(∀x (p(x) ↔ q(x)) and (∀x p(x) ↔ ∀x q(x)) are logically equivalent or not justify the answer
1. (∀x (p(x) → q(x)) and (∀x p(x) → ∀x q(x))2.∃x p(x)∧∃x q(x) and ∃x (p(x)∧q(x))3.(∀x (p(x) ↔ q(x)) and (∀x p(x) ↔ ∀x q(x))are logically eq...
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0 votes
1 answer
592
recurrence relation
Which recurrence relation satisfy the sequence: 2, 3, 4, . . ., for n ≥ 1. A ) T(N) = 2 T(N-1) - T(N-2) B)T(N) = T(N-1) + T(N-2) C)T(N) = N+1 D) None of these
Which recurrence relation satisfy the sequence: 2, 3, 4, . . ., for n ≥ 1.A ) T(N) = 2 T(N-1) - T(N-2) B)T(N) = T(N-1) + T(N-2)C)T(N) = N+1D)None of these
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3 votes
1 answer
594
Mathematical Logic Ques:Self doubt
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$ or $2)\sim \left ( \forall S(x)\vee V(x) \right )$ Among $1)$ and $2)$, which one is correct? and why?
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$or$2)\sim \left ( \forall S(x)\vee V(x) \rig...
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2 votes
1 answer
595
Number of edges in Hasse Diagram
Let G be the graph defined as the the Hasse diagram for the ⊆ relation on the set P{1,2,...,n}.(n>0).Determine how many edges are there in G.
Let G be the graph defined as the the Hasse diagram for the ⊆ relation on the set P{1,2,...,n}.(n>0).Determine how many edges are there in G.
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0 votes
2 answers
596
Kenneth Rosen Edition 7 Exercise 1.4 Question 11 (Page No. 53)
Let $P(x)$ be the statement “$x = x^2$”. If the domain consists of the integers, what are these truth values? $P(0)$ $P(1)$ $P(2)$ $P(-1)$ $\exists xP(x)$ $\forall x P(x)$
Let $P(x)$ be the statement “$x = x^2$”. If the domain consists of the integers, what are these truth values?$P(0)$$P(1)$$P(2)$$P(-1)$$\exists xP(x)$$\forall x P(x)$
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2 votes
1 answer
598
Probability
Prabha is working in a software company. Her manager is running a dinner for those employees having atleast one son. If Prabha is invited to the dinner and everyone knows she has two children. What is the probability that they are both boys?
Prabha is working in a software company. Her manager is running a dinner for those employees having atleast one son. If Prabha is invited to the dinner and everyone knows...
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0 votes
3 answers
599
Express the statement in logical expression
Express the statement "Everyone has exactly one best friend" as a logical expression involving predicates,quantifiers with a domain consisting of all people,and logical connectives without using uniqueness quantifier. I am confused pleased explain it
Express the statement "Everyone has exactly one best friend" as a logical expression involving predicates,quantifiers with a domain consisting of all people,and logical c...
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1 votes
1 answer
600
Mathematical Logic: Doubt on meaning of statement
The notation $\exists ! x P(x)$ denotes the proposition there exists a unique $x$ such that $P(x)$ ... What will be answer here?? Is the assumption only for left hand side and not right hand side??
The notation $\exists ! x P(x)$ denotes the proposition “there exists a unique $x$ such that $P(x)$ is true”. Give the truth values of the following statements : I)${...
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