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Recent questions and answers in Mathematical Logic
45
votes
8
answers
1
GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE
KG
answered
in
Mathematical Logic
May 25
by
KG
8.5k
views
gatecse-2017-set1
mathematical-logic
propositional-logic
1
vote
1
answer
2
GATE CSE 1988 | Question: 14ii
Consider the following well-formed formula: $\exists x \forall y [ \neg \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Show using resolution principle that the well-formed formula, given above, cannot be satisfied for any interpretation.
Ayushpal
answered
in
Mathematical Logic
May 24
by
Ayushpal
427
views
gate1988
descriptive
first-order-logic
clausal-form
out-of-gate-syllabus
89
votes
9
answers
3
GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
uttsav1998
answered
in
Mathematical Logic
May 23
by
uttsav1998
15.6k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
0
votes
1
answer
4
self doubts
a’b’c+a’bc’+abc=?
Eswar01
answered
in
Mathematical Logic
May 23
by
Eswar01
54
views
self-doubt
0
votes
1
answer
5
Find the value of [v]e wherev is a vector space and e is a list of polynomials
ankitgupta.1729
answered
in
Mathematical Logic
May 18
by
ankitgupta.1729
57
views
linear-algebra
7
votes
2
answers
6
UGC NET CSE | December 2018 | Part 2 | Question: 1
In mathematical logic, which of the following are statements? There will be snow in January. What is the time now? Today is Sunday. You must study Discrete mathematics Choose the correct answer from the code given below: i and iii i and ii ii and iv iii and iv
itsayush007
answered
in
Mathematical Logic
May 17
by
itsayush007
3.8k
views
ugcnetcse-dec2018-paper2
mathematical-logic
1
vote
1
answer
7
in proposition i have doubt in implication statement in p->q can i assume p->q is false when p is false ?
Samaroha
answered
in
Mathematical Logic
May 15
by
Samaroha
64
views
discrete-mathematics
propositional-logic
36
votes
7
answers
8
GATE CSE 2009 | Question: 23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
Soumen Mondal 1
answered
in
Mathematical Logic
May 14
by
Soumen Mondal 1
6.4k
views
gatecse-2009
mathematical-logic
easy
first-order-logic
0
votes
0
answers
9
Let (1 + x)n = C0 + C1x + C2x2 + . . . + Cnxn, n being a positive integer. Then find the value of ( 1 + C0 C1 ) ( 1 + C1 C2 ) . . . ( 1 + Cn−1 Cn
JISAANNAGEORGE
asked
in
Mathematical Logic
May 11
by
JISAANNAGEORGE
46
views
mathematical-logic
2
votes
1
answer
10
TIFR CSE 2023 | Part B | Question: 1
Consider the following two statements: $\text{(P)}$ The current population of Bhutan is greater than the current population of India. $\text{(Q)}$ The Moon is smaller than the Earth. Clearly, $\text{(P)}$ is false, while $\text{(Q)}$ is true. ... $\neg(\text{P} \Rightarrow \text{Q})$ $\text{P} \Leftrightarrow \text{Q}$ None of the above
csayan
answered
in
Mathematical Logic
May 11
by
csayan
151
views
tifr2023
mathematical-logic
propositional-logic
0
votes
0
answers
11
Generating Functions
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
May 11
by
Çșȇ ʛấẗẻ
31
views
discrete-mathematics
kenneth-rosen
generating-functions
0
votes
0
answers
12
Hasse Diagram
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
May 11
by
Çșȇ ʛấẗẻ
38
views
hasse-diagram
set-theory&algebra
lattice
graph-theory
0
votes
0
answers
13
Expectation of Random Variable
Consider a quiz where a person is given two questions and he must decide which question to answer first. Question 1 will be answered correctly with probability of 0.8 and the person will then receive as prize \ ... we sum P(X=0) + P(X=100) + P(X= 200) + P(X=300) = 2 Where I am getting wrong?
Chaitanya Kale
asked
in
Mathematical Logic
May 10
by
Chaitanya Kale
54
views
probability
expectation
random-variable
engineering-mathematics
18
votes
3
answers
14
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 12
Two compound propositions are logically equivalent if they have the same truth table. For example, the following two compound propositions are logically equivalent: $\mathrm{p} \rightarrow \mathrm{q}$ ... propositional variables, how many compound propositions are there that are Not logically equivalent to each other?
ayush_27
answered
in
Mathematical Logic
May 9
by
ayush_27
303
views
goclasses2024_wq5
numerical-answers
goclasses
mathematical-logic
propositional-logic
2-marks
0
votes
1
answer
15
Proposition Logic doubt
Given: (p$ \vee$ q) is True. Find the truth value of statements, 1. p is false or q is true. (Can't determine) 2. If p is false then q is true. (True) is my answer correct?????
Durgesh_7979
answered
in
Mathematical Logic
May 7
by
Durgesh_7979
170
views
discrete-mathematics
propositional-logic
mathematical-logic
3
votes
1
answer
16
Kenneth Rosen Edition 7 Exercise 1.6 Question 28 (Page No. 80)
Use rules of inference to show that if $\forall x (P(x) \vee Q(x))$ and $\forall x ((\sim P(x) \wedge Q(x)) \rightarrow R(x))$ are true, then $\forall x (\sim R(x) \rightarrow P(x))$ is also true, where the domains of all quantifiers are the same.
thehitchh1ker
answered
in
Mathematical Logic
May 7
by
thehitchh1ker
252
views
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
0
votes
1
answer
17
#discrete mathematics #1st order logic
Prove or disprove (a) ∃x(P(x) ↔ Q(x)) → ¬∀xQ(x) ∨ ∃xP(x).
d0t
answered
in
Mathematical Logic
May 6
by
d0t
96
views
first-order-logic
mathematical-logic
discrete-mathematics
80
votes
5
answers
18
GATE CSE 2004 | Question: 23, ISRO2007-32
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
Akash 15
answered
in
Mathematical Logic
May 1
by
Akash 15
12.4k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
0
votes
1
answer
19
Applied Mathematics-IB
Use the Squeeze Theorem to determine the value of $\lim_{x\rightarrow 0} x^{4}\sin (\frac{\pi}{x}).$x^{4}\sin (\frac{\pi}{x}).$
artim
answered
in
Mathematical Logic
Apr 30
by
artim
36
views
limits
50
votes
10
answers
20
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
KG
answered
in
Mathematical Logic
Apr 28
by
KG
9.8k
views
gatecse-2017-set2
mathematical-logic
propositional-logic
0
votes
0
answers
21
Applied Mathematics-IB
Determine all the number(s) c which satisfy the conclusion of Roles' Theorem for the given function and interval $f(x)=x^{2}-2x-8 $ on $ [-1,3]$
Hailemariam
asked
in
Mathematical Logic
Apr 28
by
Hailemariam
52
views
limits
0
votes
0
answers
22
Applied Mathematics-IB
sketch the graph of $h(x)=-(x+4)^{3}$ and identify all the relative extrema and absolute extrema of the function.
Hailemariam
asked
in
Mathematical Logic
Apr 28
by
Hailemariam
15
views
limits
0
votes
1
answer
23
Applied Mathematics-IB
Given that $7x\leq f\left ( x \right )\leq 3x^{2}+2$ for all determine the value of $\lim x\rightarrow 0 f(x)$
artim
answered
in
Mathematical Logic
Apr 28
by
artim
37
views
limits
0
votes
0
answers
24
Applied Mathematics-IB
1. Evaluate $x\rightarrow 5 lim (10)+\mid x-5\mid$
Hailemariam
asked
in
Mathematical Logic
Apr 28
by
Hailemariam
49
views
mathematical-logic
10
votes
2
answers
25
GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 13
Consider the following list of $137$ statements: $\left(S_1\right): $ There is exactly $1$ false statement in this list. $\left(S_2\right): $ There are exactly $2$ ... true. It is possible that more than one statement in this list is true. Exactly one statement in this list is true.
zoy123
answered
in
Mathematical Logic
Apr 27
by
zoy123
203
views
goclasses2024_wq7
goclasses
mathematical-logic
propositional-logic
2-marks
51
votes
7
answers
26
GATE CSE 2003 | Question: 72
The following resolution rule is used in logic programming. Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$ Which of the following statements related to this rule is FALSE? $((P ∨ R)∧(Q ∨ ¬R))⇒(P ∨ Q)$ ... if $(P ∨ R)∧(Q ∨ ¬R)$ is satisfiable $(P ∨ Q)⇒ \text{FALSE}$ if and only if both $P$ and $Q$ are unsatisfiable
prajjwal_191
answered
in
Mathematical Logic
Apr 25
by
prajjwal_191
10.2k
views
gatecse-2003
mathematical-logic
normal
propositional-logic
0
votes
1
answer
27
Discrete Maths Partial ordered set
[D6 , / ] is a poset ?
Ashutosh_17
asked
in
Mathematical Logic
Apr 20
by
Ashutosh_17
68
views
discrete-mathematics
1
vote
3
answers
28
Discrete Mathematics | Predicate Logic
Which of the following conclusion can be drawn from the following premises $\left ( 1 \right )\sim P\vee Q\rightarrow R$ $\left ( 2 \right )S\vee \sim Q$ $\left ( 3 \right )\sim T$ $\left ( 4 \right )P\rightarrow T$ $\left ( 5 \right )\sim P\wedge R\rightarrow \sim S$ $C1: P$ $C2: \sim Q$ $C3: Q\wedge R$ C1 only C2 only C2 & C3 only C1 & C2 only
Jay Patel 009
asked
in
Mathematical Logic
Apr 18
by
Jay Patel 009
143
views
discrete-mathematics
mathematical-logic
first-order-logic
3
votes
2
answers
29
Discrete Mathematics | Propositional Logic | Test 2 | Question: 1
Let $\Phi$ be a well-formed formula having atleast one occurrence of atomic variable $x.$ Consider $\Psi$ be any formula. Now, $_x\Phi_{\Psi}$ is the formula obtained by replacing each occurrence of $x$ by $\Psi$ in $\Phi$ and ... Only (i) is correct Only (ii) is correct Both (i) and (ii) are correct None of the above
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
127
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
1-mark
1
vote
1
answer
30
Discrete Mathematics | Propositional Logic | Test 2 | Question: 2
Consider the following argument: Either logic is difficult, or not many students like it. If mathematics is easy, then logic is not difficult. $\textit{Therefore,}$ if many students like logic, mathematics is not ... argument then $P \rightarrow Q$ is a tautology Validity of the given argument can't be determined
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
67
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
1
vote
1
answer
31
Discrete Mathematics | Propositional Logic | Test 2 | Question: 3
Suppose we have to construct a formula that expresses the truth function $\phi$ ... The formula that $\phi$ expresses is $\neg p \rightarrow ((p \rightarrow \neg p) \rightarrow (\neg p \rightarrow p))$
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
104
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
1
vote
1
answer
32
Discrete Mathematics | Propositional Logic | Test 2 | Question: 4
Consider a conditional statement $P \rightarrow Q.$ The proposition $Q \rightarrow P$ is called the $\textit{converse}$ of $P \rightarrow Q.$ The proposition $\neg Q \rightarrow \neg P$ ... If the converse is true, then the inverse is also logically true. (P and Q are distinct atomic sentences)
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
115
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
0
votes
1
answer
33
Discrete Mathematics | Propositional Logic | Test 2 | Question: 5
A compound proposition is $\textit{satisfiable}$ if there is an assignment of truth values to its variables that makes it true. When no such assignments exists, that is, when the compound proposition is false for all assignments of ... but not valid. Hence, it is a contingency where $P,Q$ and $R$ are distinct atomic propositions.
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
63
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
5
votes
2
answers
34
Discrete Mathematics | Propositional Logic | Test 2 | Question: 6
How many assignments of truth values to distinct $P_1,P_2,P_3,...,P_n$ with $n \geq 5$ ... $\textbf{Hint}:$ Try to construct the recurrence for the given problem and then solve it)
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
242
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
0
votes
1
answer
35
Discrete Mathematics | Propositional Logic | Test 2 | Question: 7
Suppose two premises are given as: $(1)$ Either Mary gives Peter his toy or Peter is going to cry. $(2)$ Mary does not give Peter his toy. Which one of the following statements is correct ? ... follows from the above two premises. Conclusion 'Peter is not going to cry' logically follows from the above two premises.
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
57
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
2
votes
1
answer
36
Discrete Mathematics | Propositional Logic | Test 2 | Question: 8
In the $\textit{theory of inference},$ we begin with a set of formulas which we call $\textit{premises/ hypotheses}$ and using some rules we obtain some other $\textit{given formula}$ ... a logical consequence of given premises Premise $(1)$ and $\neg C$ does not tautologically imply $S$
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
100
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
2
votes
2
answers
37
Discrete Mathematics | Propositional Logic | Test 2 | Question: 9
To decide an argument is $\textit{valid}$ with $n$ distinct premises as $P_1,P_2,...,P_n$ and conclusion $C$, we need to decide whether $(P_1 \wedge P_2 \wedge...\wedge P_n) \rightarrow C$ is tautology or not. Which of the ... $R,$ then we $\textit{can't}$ infer $R \rightarrow S$ from $P_1,P_2,...,P_n.$
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
156
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
1
vote
1
answer
38
Discrete Mathematics | Propositional Logic | Test 2 | Question: 10
Premises $P_1,P_2,...,P_n$ infer/derive a conclusion $Q$ if and only if the conditional $(P_1 \wedge P_2 \wedge...\wedge P_n) \rightarrow Q$ is a tautology. Consider the following statements: From $P$ ... $P$, $Q$ and $R$ are distinct atomic sentences ) Number of correct statements are ______
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
102
views
testsbyankitg-dm-2
numerical-answers
mathematical-logic
propositional-logic
2-marks
1
vote
2
answers
39
Discrete Mathematics | Propositional Logic | Test 2 | Question: 11
Consider the following argument: If either wages or prices are raised, there will be inflation. If there is inflation, then either Congress must regulate it or the people will suffer. If the people suffer, Congressmen will ... $P \rightarrow Q$ is a tautology. Validity of the given argument can't be determined.
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
120
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
4
votes
3
answers
40
Discrete Mathematics | Propositional Logic | Test 2 | Question: 12
Two sentences are said to be $\textit{contradictory}$ if one is negation of the other. A $\textit{contradiction}$ is a conjunction of two contradictory sentences i.e. it is a conjunction of the form $S \wedge \neg S.$ A set ... Only $(ii)$ is correct Both $(i)$ and $(ii)$ are correct None of the above
ankitgupta.1729
asked
in
Mathematical Logic
Apr 16
by
ankitgupta.1729
206
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
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Recent questions and answers in Mathematical Logic
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