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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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Highest voted questions in Mathematical Logic

1 votes
1 answer
921
permutation and combination
A roller coaster has five cars, each containing four seats, two in front and two in back. There are 20 people ready for a ride. In how many ways can the ride begin? What if a certa:in two people want to sit in different cars?
A roller coaster has five cars, each containing four seats, two in front and twoin back. There are 20 people ready for a ride. In how many ways can the ridebegin? What if...
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1 votes
1 answer
922
Sub-groups
Find all subgroups of a cyclic group of order 12. Also what is the number of generators? Doubt: I got subgroups as a, a2, a3, a4, a6 and a12. How to identify the identity element among these?
Find all subgroups of a cyclic group of order 12. Also what is the number of generators?Doubt: I got subgroups as a, a2, a3, a4, a6 and a12. How to identify the identity ...
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1 votes
1 answer
923
solving equation
-X^3 + X^2 -X -1=0 from this how do we find possible values of X
-X^3 + X^2 -X -1=0from this how do we find possible values of X
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1 votes
2 answers
924
self doubt
Find the total number of equivalent relations possible on a set S={4,7,1}. is there any other way to solve it without using bell formula?
Find the total number of equivalent relations possible on a set S={4,7,1}.is there any other way to solve it without using bell formula?
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1 votes
2 answers
925
doubt . which statement is accurate ?
cardinality of sets is number of elements in set -- wikipedia but in many sites they wrote cardinality is no. of DISTINCT elements in the set ? which is correct
cardinality of sets is number of elements in set wikipediabut in many sites they wrote cardinality is no. of DISTINCT elements in the set ?which is correct
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1 votes
0 answers
926
doubt
Is a null matrix also a diagonal matrix? i read somewhere atleast one element in diagonal should be non zero to be a diagonal matrix //provided null matrix will be square and can a null square matrix be a scalar matrix ?
Is a null matrix also a diagonal matrix? i read somewhere atleast one element in diagonal should be non zero to be a diagonal matrix //provided null matrix will be squar...
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1 votes
1 answer
927
sets and relations
What are all the possible relations over a set A{1,2}? Pease explain in detail.
What are all the possible relations over a set A{1,2}? Pease explain in detail.
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1 votes
2 answers
930
Limit
The limit x->0 sin[2x/3]/x is
The limit x->0 sin[2x/3]/x is
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1 votes
0 answers
931
explain ?
how many different words can be formed from letter of word HARYANA 7! / 3! = 840 according to rd sharma but it should be 840-1 = 839 ,because in question we have to find different everywhere they didnot subtract 1
how many different words can be formed from letter of word HARYANA7! / 3! = 840 according to rd sharma but it should be 840-1 = 839 ,because in question we have to ...
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1 votes
1 answer
933
Propositional function doubt
The Number of n-variable propositional function ? a. 2^2^n. b.2^n^2 c.2^n d. n^2 Can any one please explain the what should be the answer and how to get it?
The Number of n-variable propositional function ?a. 2^2^n.b.2^n^2c.2^nd. n^2Can any one please explain the what should be the answer and how to get it?
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1 votes
0 answers
934
Discrete mathematics
Proofs questions are asked in mathematical logic gate?
Proofs questions are asked in mathematical logic gate?
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1 votes
1 answer
936
Limits
can you please solve lt x->1 x^3-x^2logx+logx-1/x^2-1 using L-Hospitals rule
can you please solve lt x->1 x^3-x^2logx+logx-1/x^2-1using L-Hospitals rule
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1 votes
0 answers
937
doubt
Given 3 characters a, b, c. Find the number of strings of length n that can be formed from these 3 characters. Given that : we can use ‘a’ as many times as we want, ‘b’ maximum once, and ‘c’ maximum twice.
Given 3 characters a, b, c. Find the number of strings of length n that can be formed from these 3 characters. Given that : we can use ‘a’ as many times as we want, �...
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1 votes
0 answers
938
limit
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1 votes
2 answers
939
eigen value
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1 votes
1 answer
940
Linear algebra
How we find eigen values from characteristics equation ? Steps please.
How we find eigen values from characteristics equation ?Steps please.
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