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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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Recent questions in Mathematical Logic

#1101
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ISI-2004-30
If the tangent at the point $P$ with co-ordinates $(h, k)$ on the curve $y^2 = 2x^3$ is perpendicular to the straight line $4x=3y$, then$(h, k) = (0,0)$(h, k) = (1/8, -1 ... $(h, k) = (1/8, -1/16)$no such point $(h, k)$ exists.
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#1102
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Propositional logic
Sagar will marry Sheela only if She is a graduate and a good cook.Which is True ?1.Sheela is a good cook but not a graduate hence Sagar will not marry ... .Sagar did not marry Sheela implies that she is neither a graduate nor a good cook.
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#1103
334
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1 answers
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ISI-2004-23
If $f(x) = x^2$ and $g(x)=x \sin x + \cos x$ then$f$ and $g$ agree at no points.$f$ and $g$ agree at exactly one point.$f$ and $g$ agree at exactly two points.$f$ and $g$ agree at more than two points.
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#1104
209
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1 answers
0 votes
ISI-2004-16
For complex numbers $z_1 = x_1 + iy_1$ and $z_2 = x_2 + iy_2$, write $z_1 \preceq z_2$ if $x_1 \leq x_2$ and $y_1 \leq y_2$. Then for all complex numbers $z$ ... $\dfrac{1-z}{1+z} \preceq 0$none of these.
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#1105
269
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1 answers
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ISI-2004-14
The inequality $\cfrac{2-gx-x^2}{1-x+x^2} \leq 3$ is true for all values of $x$ if and only if$1 \leq g \leq 7$-1 \leq g \leq 1$-6 \leq g \leq 7$-1 \leq g \leq 7$
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#1106
1.1k
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1 answers
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PGEE Sample paper
More than one option can be correct
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#1107
3.2k
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0 answers
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PGEE Sample paper
More than one option can be correct
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#1108
170
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1 answers
0 votes
ISI-2004-10
The equation $P(x) = \alpha$ where $P(x) = x^4 + 4x^3 – 2x^2 – 12x$ has four distinct real roots if and only if $P(-3) < \alpha$P(-1) > \alpha$P(-1) < \alpha$P(-3) < \alpha < P(-1)$
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#1109
233
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1 answers
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ISI-2004-11
If $a_1,a_2, \dots,a_n$ are positive real numbers, then$\frac{a_1}{a_2} + \frac{a_2}{a_3} + \cdots + \frac{a_{n-1}}{a_n}+\frac{a_n}{a_1}$is always$\geq n$\leq n$\leq n^{1/n}$none of the above.
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#1110
213
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1 answers
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ISI-2004-8
If $\alpha _1, \alpha _2,\dots,\alpha _n$ be the roots of $x^n + 1 = 0$, then $(1-\alpha _1)(1-\alpha _2)\dots(1-\alpha _n)$ is equal to$1$0$n$2$
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#1111
249
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ISI-2014-SAMPLE-25
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#1112
154
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0 answers
1 votes
ISI-SAMPLE-2014-22
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#1113
1.1k
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0 answers
1 votes
Propositional Logic
Number of nonequivalent propositional functions ( different truth tables ) possible with 'n' atomic propositions is ? and explain alsoa) $2^n$b) $n^2$c) 2^2^n (means 2 raise to power 2 raise to power n)d) 2^n^2
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#1114
912
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1 answers
0 votes
Generating functions
In generating function i studied from books i didn't understand two things1. How to apply generating functions for solving recurrence relation2. Generating functions for solving Permutations Can anybody explain it with an example ?
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#1115
144
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0 answers
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ISI-SAMPLE-2014
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#1116
199
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2 answers
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ISI-SAMPLE-2014
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#1117
426
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0 answers
0 votes
Predicate Prperties
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#1118
331
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2 answers
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ISI-2014-SAMPLE-18
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#1119
235
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0 answers
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ISI-SAMPLE-2014-17
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#1120
466
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2 answers
0 votes
ISI-SAMPLE-2014-15
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