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Syllabus: Propositional and first order logic.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022}& \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}& 0 & 1&1&0&0&0&2&1&1&1&0&0.7&2
\\\hline\textbf{2 Marks Count}&0 & 0&0&1&1&1&1&0&0&1&0&0.5&1
\\\hline\textbf{Total Marks}& 0 & 1&1&2&2&2&4&1&1&3&\bf{0}&\bf{1.7}&\bf{4}\\\hline
\end{array}}}$$

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Highest voted questions in Mathematical Logic

1 votes
0 answers
931
Ace previous paper on propositional logic
Gate 2006 question on binary relation
Gate 2006 question on binary relation
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1 votes
1 answer
933
Set theory doubt
Let P and Q be any two equivalence relation on empty set s then choose the correct one a)pUq ,p∩q both are equivalence relations b)pUq is an equivalence relation c)p∩q is an equivalence relation d)Neither pUq ,p∩q both are equivalence relations
Let P and Q be any two equivalence relation on empty set s then choose the correct onea)pUq ,p∩q both are equivalence relationsb)pUq is an equivalence relationc)p∩q i...
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1 votes
1 answer
934
GATE PREV
∃x(p(x)∧q(x))⟹(∃xp(x)∧∃xq(x)) a)It is false because ∃ is not distributive over ∧ b) If we say LHS is false ,then then entire statement is true. WHICH ONE I CHOOSE ?
∃x(p(x)∧q(x))⟹(∃xp(x)∧∃xq(x))a)It is false because ∃ is not distributive over ∧b) If we say LHS is false ,then then entire statement is true.WHICH ONE I C...
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1 votes
2 answers
935
trace of matrix
If $\lambda^3 - 6\lambda^2 -\lambda +22=0$ is a characteristic equation of $3\ X\ 3$ diagonal matrix, then trace of matrix is
If $\lambda^3 - 6\lambda^2 -\lambda +22=0$ is a characteristic equation of $3\ X\ 3$ diagonal matrix, then trace of matrix is
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1 votes
0 answers
937
answer should be does not exist , but in rd sharma answer is 1/ 8 root(3) how -_-
limit root ( 1 + root (2+x) - root (3) ) / ( x -2 ) x --->2
limit root ( 1 + root (2+x) - root (3) ) / ( x -2 ) x ->2
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1 votes
1 answer
938
#Combinatorics
At any time, the total number of persons on earth who have shaken hands an odd number of times has to be The answer provided is even number but cannot understand how
At any time, the total number of persons on earth who have shaken hands an odd number of times has to be The answer provided is even number but cannot understand how
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1 votes
1 answer
939
Mathematical Logic question
Which among them are valid? How to approach such questions ?
Which among them are valid?How to approach such questions ?
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1 votes
1 answer
940
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
941
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
942
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
943
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
944
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
945
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
946
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
949
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
950
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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