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Webpage for Mathematical Logic
Important Question Types:
Checking validity of First Order Logic Statements
Checking validity of Propositional Logic
Recent questions tagged mathematical-logic
3
votes
3
answers
241
GATE 2008 | Question 21
I have been trying to solve the question GATE CSE 2008 Question. Are the following two representations logically equivalent ? $\beta \rightarrow (\exists x, \alpha (x))$ $\exists x, \beta \rightarrow \alpha (x)$
I have been trying to solve the question GATE CSE 2008 Question.Are the following two representations logically equivalent ?$\beta \rightarrow (\exists x, \alpha (x))$$\e...
ParthPratim
969
views
ParthPratim
asked
Nov 3, 2022
Mathematical Logic
gatecse-2008
mathematical-logic
first-order-logic
normal
+
–
0
votes
1
answer
242
Translate the given statement into propositional logicexpressions:“A man qualifies for the marathon if his best previous time is less than 3 hours and a woman qualifies for the marathon if her best previous time is less than 3.5 hours.
VASEEMUN
690
views
VASEEMUN
asked
Oct 29, 2022
Mathematical Logic
discrete-mathematics
mathematical-logic
propositional-logic
+
–
0
votes
2
answers
243
is this argument valid: {P->Q , Q->R}-> R'
Shivam_j
1.1k
views
Shivam_j
asked
Oct 3, 2022
Mathematical Logic
mathematical-logic
+
–
0
votes
3
answers
244
Predicate Translation
S(x): x is a Student P(x): x is a Professor A(x, y): x has asked a question to y Domain not given, so we have to think about default domain Q1) Translate There is a student who has asked every professor a question Q2) Translate ... a professor who has been asked a question by every student Q4) Translate There is a student who has been asked a question by every professor
S(x): x is a StudentP(x): x is a ProfessorA(x, y): x has asked a question to yDomain not given, so we have to think about default domainQ1) Translate “There is a studen...
prithatiti
655
views
prithatiti
asked
Sep 6, 2022
Mathematical Logic
propositional-logic
mathematical-logic
discrete-mathematics
+
–
0
votes
0
answers
245
Mathematics for Natural Science
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$
kidussss
315
views
kidussss
asked
Jul 29, 2022
Combinatory
discrete-mathematics
mathematical-logic
calculus
set-theory
+
–
0
votes
1
answer
246
Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
kidussss
234
views
kidussss
asked
Jul 29, 2022
Combinatory
discrete-mathematics
mathematical-logic
calculus
set-theory
+
–
0
votes
1
answer
247
Mathematics for Natural Science
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$
kidussss
234
views
kidussss
asked
Jul 29, 2022
Combinatory
discrete-mathematics
mathematical-logic
calculus
set-theory
+
–
0
votes
1
answer
248
Mathematics for Natural Science
Suppose $x, y, z > 1$ are integers, let: $p(x,y)$ : $x$ is a factor of $y$ $q(x,y,z)$ : $z$ = $\text{GCD}(x,y)$ $r(x)$ : $x$ is prime. Check if the following argument is valid or not. $(\forall x \exists y)p(x,y) \implies r(x)$ ... $(\exists x)(\forall y)(p(x,y) \lor r(x))$ $\therefore (\forall y)(\exists z)(\exists x)q(x,y,z)$
Suppose $x, y, z 1$ are integers, let:$p(x,y)$ : $x$ is a factor of $y$$q(x,y,z)$ : $z$ = $\text{GCD}(x,y)$$r(x)$ : $x$ is prime.Check if the following argument is valid...
kidussss
352
views
kidussss
asked
Jul 29, 2022
Mathematical Logic
mathematical-logic
discrete-mathematics
+
–
0
votes
0
answers
249
quantifiers to express each of these statements.
Let P(x) be the statement x has a cell phone and M(x,y) be the statement x and y have texted over the cell phone, where the domain for the variables x and y consists of all students in your class. Use quantifiers to ... other student in your class. c) Someone in your class has a cell phone but has not texted with anyone else in your class.
Let P(x) be the statement “x has a cell phone” and M(x,y) be the statement “x and y have texted over the cell phone,” where the domain for the variables x and y c...
hussain yasir
464
views
hussain yasir
asked
Jul 7, 2022
Mathematical Logic
quantifiers
mathematical-logic
first-order-logic
+
–
3
votes
1
answer
250
GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 2
Assume the following predicate and constant symbols.$W(x,y) :\; x$ wrote $y$$L(x,y) :\; x$ is longer than $y$$h :$ Hardy$a :$ Austen$j :$ Jude the Obscure$p :$ Pride and ...
GO Classes
571
views
GO Classes
asked
May 12, 2022
Mathematical Logic
goclasses_wq10
goclasses
mathematical-logic
first-order-logic
1-mark
+
–
2
votes
1
answer
251
GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 8
Let the universe for all quantified variables be the set of all novels. Assume the following predicates and constant symbols:$W(x,y) :\; x$ wrote novel $y$$L(x,y) : \;x$ ...
GO Classes
422
views
GO Classes
asked
May 12, 2022
Mathematical Logic
goclasses_wq10
goclasses
mathematical-logic
first-order-logic
2-marks
+
–
3
votes
1
answer
252
GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 9
Working with a unary predicate symbol, $P,$ a binary predicate symbol $Q$ and a unary function symbol $f,$ consider the following interpretation $M,$ given by,Universe $A...
GO Classes
334
views
GO Classes
asked
May 12, 2022
Mathematical Logic
goclasses_wq10
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
+
–
3
votes
1
answer
253
GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 10
Recall that a "sentence/proposition" is a predicate logic formula that has no free variables.In predicate logic, a set of sentences is satisfiable iff there is some inter...
GO Classes
299
views
GO Classes
asked
May 12, 2022
Mathematical Logic
goclasses_wq10
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
+
–
2
votes
2
answers
254
GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 4
How many rows appear in a truth table for this compound proposition? $p \rightarrow \neg p$
How many rows appear in a truth table for this compound proposition?$p \rightarrow \neg p$
GO Classes
454
views
GO Classes
asked
May 2, 2022
Mathematical Logic
goclasses_wq2
numerical-answers
goclasses
mathematical-logic
propositional-logic
1-mark
+
–
4
votes
4
answers
255
GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 5
How many rows appear in a truth table for this compound proposition? $(p \wedge r \wedge t) \leftrightarrow (q \wedge t)$
How many rows appear in a truth table for this compound proposition?$(p \wedge r \wedge t) \leftrightarrow (q \wedge t)$
GO Classes
625
views
GO Classes
asked
May 2, 2022
Mathematical Logic
goclasses_wq2
numerical-answers
goclasses
mathematical-logic
propositional-logic
1-mark
+
–
0
votes
1
answer
256
kenneth h rosen chapter 1 section 1.5 PRENEX NORMAL FORM in excercise 1.5
can this topic “PRENEX NORMAL FORM(PNF) ” is necsesary for gate or just i skip this topic.
can this topic “PRENEX NORMAL FORM(PNF) ” is necsesary for gate or just i skip this topic.
ykrishnay
281
views
ykrishnay
asked
Apr 20, 2022
Mathematical Logic
discrete-mathematics
engineering-mathematics
propositional-logic
kenneth-rosen
mathematical-logic
+
–
0
votes
0
answers
257
kenneth h rosen chapter 1 section section 1.5 nested quatnifiers excercise 49
49. a) Show that ∀xP (x) ∧ ∃xQ(x) is logically equivalent to ∀x∃y (P (x) ∧ Q(y)), where all quantifiers have the same nonempty domain. b) Show that ∀xP (x) ∨ ∃xQ(x) is equivalent to ∀x∃y (P (x) ∨ Q(y)), where all quantifiers have the same nonempty domain. please anybody tell how to prove this logical equivalency ?
49. a) Show that ∀xP (x) ∧ ∃xQ(x) is logically equivalentto ∀x∃y (P (x) ∧ Q(y)), where all quantifiers havethe same nonempty domain.b) Show that ∀xP (x) ∨...
ykrishnay
356
views
ykrishnay
asked
Apr 20, 2022
Mathematical Logic
discrete-mathematics
propositional-logic
engineering-mathematics
kenneth-rosen
mathematical-logic
+
–
0
votes
0
answers
258
kenneth h rosen chapter 1 section 1.5 nested quantifiers excercise 1.5 question 48
Show that ∀xP (x) ∨ ∀xQ(x) and ∀x∀y(P (x) ∨ Q(y)), where all quantifiers have the same nonempty domain, are logically equivalent. (The new variable y is used to combine the quantifications correctly.)
Show that ∀xP (x) ∨ ∀xQ(x) and ∀x∀y(P (x) ∨ Q(y)),where all quantifiers have the same nonempty domain,are logically equivalent. (The new variable y is used to...
ykrishnay
519
views
ykrishnay
asked
Apr 20, 2022
Mathematical Logic
discrete-mathematics
propositional-logic
engineering-mathematics
kenneth-rosen
mathematical-logic
+
–
0
votes
0
answers
259
kenneth h rosen chapter 1 section nested quantifers excercise 1.5 question 40
Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all integers. a) ∀x∃y(x = 1/y) b) ∀x∃y(y^2 − x < 100)
Find a counterexample, if possible, to these universallyquantified statements, where the domain for all variablesconsists of all integers.a) ∀x∃y(x = 1/y)b) ∀x∃y(...
ykrishnay
312
views
ykrishnay
asked
Apr 19, 2022
Mathematical Logic
discrete-mathematics
propositional-logic
mathematical-logic
engineering-mathematics
kenneth-rosen
+
–
0
votes
0
answers
260
kenneth h rosen chapter 1 section "Nested quantifers" excercise 1.5 question 26's g
Let Q(x, y) be the statement “x + y = x − y.” If the do- main for both variables consists of all integers, what are the truth values? g) ∃y∀xQ(x, y) Basically i done all the subquestions (a,b,c,d,e,f,h,i) from this question but confused in g subquestion please give answer
Let Q(x, y) be the statement “x + y = x − y.” If the do-main for both variables consists of all integers, what arethe truth values?g) ∃y∀xQ(x, y)Basically i don...
ykrishnay
185
views
ykrishnay
asked
Apr 18, 2022
Mathematical Logic
discrete-mathematics
mathematical-logic
propositional-logic
engineering-mathematics
kenneth-rosen
+
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