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Syllabus: Propositional and first order logic.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \textbf{Year}& \textbf{2026 - 1}& \textbf{2026 - 2}& \textbf{2025 - 1}& \textbf{2025 - 2}& \textbf{2024 - 1}& \textbf{2024 - 2}& \textbf{2023}& \textbf{2022}& \textbf{2021 - 1}& \textbf{2021 - 2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}\\\hline \textbf{1 Mark Count}&0&1&0&1&0&1&1&0&1&1&0&0.6&1\\\hline \textbf{2 Marks Count}&0&0&1&0&0&0&0&0&0&0&0&0.1&1\\\hline \textbf{Total Marks}&0&1&2&1&0&1&1&0&1&1&\bf{0}&\bf{0.8}&\bf{2}\\\hline \end{array}}}$$

Recent questions in Mathematical Logic

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Question Description:I am a 3rd-year engineering student preparing for GATE. I have not studied Engineering Mathematics (EM) and Discrete Mathematics (DM) properly yet.I ...
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60
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Expected number of tosses to get THT ?
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179
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What is the most reliable way to find the logical equivalent for either.. or.. questions? Either I take metro or I take bus - for this question the answer is p V qEither...
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176
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You can access the internet from campus only if you are a computer science major or you are not a freshmanx: You can access the internet from campusy: you are a computer ...
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1 1 answer
98
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a->b->c is given Which way is preferred to solve it a->(b->c) or (a->b)->c
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2 2 answers
119
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1 1 answer
105
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I go only if you stay.What is the converse of this propsition?
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1 answers 1 answer
189
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An $n \times n$ grid of points (vertices) is given. Starting from the top-left point of the grid, a person can move only one step to the right or one step downward along ...
1 1 vote
2 answers 2 answers
165
165 views
An $n \times n$ grid consists of $n$ rows and $n$ columns of square cells. Starting from the top-left corner of the grid, a person can move only one step to the right or ...
0 0 votes
1 1 answer
118
118 views
For universal quantifiers we use implication, A - B(All A's are B's).for this it's true.But in this case it's also being true for A being false.Then how is this true ??...
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1 1 answer
87
87 views
I don't understand how we came up with the formula P(sum = 5) / P(sum = 5) + P(sum = 7)
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1 1 answer
147
147 views
Let $A$ and $B$ be finite non-empty sets and let $f:A\to B$ be a function. Match $\textbf{List-I}$ with $\textbf{List-II}$.$$\begin{array}{lcl} \mathbf{List-I} && \mathbf...
1 1 vote
1 1 answer
143
143 views
Let $A,B,C$ be non-empty sets. Let $g:A\to B$ and $f:B\to C$ be functions. The composition $f\circ g$ always exists. For the reverse composition $g\circ f$ to exist as a ...
0 0 votes
1 1 answer
105
105 views
Let $A,B,C$ be finite non-empty sets and let $f:A\to B$ and $g:B\to C$ be functions. Suppose $g\circ f:A\to C$ is bijective. Which of the following statements must be tru...
1 1 vote
1 1 answer
128
128 views
Let $A$ and $B$ be finite non-empty sets such that $|A|=m$ and $|B|=n$, where $1\le m\le n$. Let $X$ be the set of all injective functions from $A$ to $B$. Let $Y=A\times...
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1 1 answer
99
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Let all logarithms be natural logarithms unless a base is written. Consider the following functions:$f:(0,\infty)\to\mathbb R$ defined by $f(x)=2\log x$. $g:(0,\infty)\to...
1 1 vote
1 1 answer
83
83 views
Let $f:\mathbb Z^+\to B$ be defined by $f(n)=\frac{n^2+n}{2n^2+2n+1}$. Which of the following statements is correct?If $B=\mathbb Q$, then $f$ is bijective. If $B={q\in\m...
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1 1 answer
92
92 views
Let $f:A\to B$ be a bijective function and let $I_A:A\to A$ and $I_B:B\to B$ denote the identity functions. Let $g:B\to A$ be any function. Consider the following stateme...
0 0 votes
1 1 answer
77
77 views
Let $f:A\to B$ be defined by $f(x)=\frac{3x-5}{2x+1}$. Which of the following choices of $A$ and $B$ makes $f$ a bijection?$A=\mathbb R$ and $B=\mathbb R$ $A=\mathbb R-{-...
0 0 votes
1 1 answer
93
93 views
Let $f:A\to B$ and $g:B\to C$ be functions, where $A,B,C$ are non-empty sets. Define $h=g\circ f:A\to C$. Consider the following statements:$p:$ If $g\circ f$ is one-to-o...