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Recent activity in Discrete Mathematics
43
votes
2
answers
1
GATE CSE 1989 | Question: 1-v
The number of possible commutative binary operations that can be defined on a set of $n$ elements (for a given $n$) is ___________.
____
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Set Theory & Algebra
Mar 24
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____
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gate1989
descriptive
set-theory&algebra
binary-operation
25
votes
4
answers
2
TIFR CSE 2010 | Part A | Question: 8
Which of the following is NOT necessarily true? { Notation: The symbol ''$\neg$''notes negation; $P (x, y)$ means that for given $x$ and $y$, the property $P(x, y)$ is true }. $(∀x∀y P(x, y)) \Rightarrow (∀y∀x P(x, y))$ ... $(∃x∀y P(x, y)) \Rightarrow (∀y∃x P(x, y))$ $(∀x∃y P(x, y)) \Rightarrow (∃y∀x P(x, y))$
Sahil5635
answered
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Mathematical Logic
Mar 24
by
Sahil5635
3.3k
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tifr2010
mathematical-logic
first-order-logic
50
votes
9
answers
3
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
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Mathematical Logic
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14.9k
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gateit-2005
mathematical-logic
first-order-logic
normal
69
votes
6
answers
4
GATE CSE 2016 Set 2 | Question: 27
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$
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Mathematical Logic
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16.8k
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gatecse-2016-set2
mathematical-logic
first-order-logic
normal
0
votes
1
answer
5
Discrete mathematics Ch 1 : Propositional logic , Topic 2 : Logical operators or connectives
Which of the following is the negation of x is even iff x is divisible by 2 a) (x is even or x is not divisible by 2) and (x is not even or x is divisible by 2) b) (x is even and x is not divisible by 2) ... is divisible by 2) c) x is not even iff x is not divisible by 2 d) x is even if x is divisible by 2
lipishagupta
answer selected
in
Mathematical Logic
Mar 21
by
lipishagupta
70
views
6
votes
1
answer
6
NIELIT Scientist B 2020 November: 84
Given the truth table of a Binary Operation \$ as follows: $ ... hline \end{array}$ Identify the matching Boolean Expression. $X \$ \neg Y$ $\neg X \$ Y$ $\neg X \$ \neg Y$ none of the options
Deepak Poonia
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Mathematical Logic
Mar 20
by
Deepak Poonia
667
views
nielit-scb-2020
mathematical-logic
propositional-logic
discrete-mathematics
41
votes
9
answers
7
GATE CSE 1996 | Question: 2.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is given by $f^{-1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{x-y}\right)$ ... $f^{-1}(x,y)=\left [ 2\left(x-y\right),2\left(x+y\right) \right ]$
ritiksri8
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in
Set Theory & Algebra
Mar 20
by
ritiksri8
9.7k
views
gate1996
set-theory&algebra
functions
normal
42
votes
8
answers
8
GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
Rohit139
answered
in
Mathematical Logic
Mar 20
by
Rohit139
17.1k
views
gatecse-2020
first-order-logic
mathematical-logic
2-marks
55
votes
6
answers
9
GATE CSE 2011 | Question: 30
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$
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Mathematical Logic
Mar 19
by
꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂
13.2k
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gatecse-2011
mathematical-logic
normal
first-order-logic
69
votes
5
answers
10
GATE CSE 2010 | Question: 30
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. Which one of the statements below expresses best the meaning of the formula, $\qquad∀x∃y∃t(¬F(x,y,t))$ Everyone can ... time No one can fool everyone all the time Everyone cannot fool some person all the time No one can fool some person at some time
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Mathematical Logic
Mar 19
by
꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂
70.1k
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gatecse-2010
mathematical-logic
easy
first-order-logic
4
votes
4
answers
11
Self Doubt: Mathematical Logic
Is the assertion "This statement is false" a proposition?
TusharRana
answered
in
Mathematical Logic
Mar 18
by
TusharRana
2.1k
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mathematical-logic
50
votes
4
answers
12
GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
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commented
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Mathematical Logic
Mar 17
by
꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂
11.7k
views
gatecse-2005
mathematical-logic
easy
first-order-logic
25
votes
7
answers
13
GATE CSE 2006 | Question: 22
Let $E, F$ and $G$ be finite sets. Let $X = (E ∩ F) - (F ∩ G)$ and $Y = (E - (E ∩ G)) - (E - F)$. Which one of the following is true? $X ⊂ Y$ $X ⊃ Y$ $X = Y$ $X - Y ≠ \emptyset$ and $Y - X ≠ \emptyset$
ritiksri8
commented
in
Set Theory & Algebra
Mar 17
by
ritiksri8
6.5k
views
gatecse-2006
set-theory&algebra
normal
set-theory
25
votes
5
answers
14
GATE CSE 2005 | Question: 8
Let $A, B$ and $C$ be non-empty sets and let $X = ( A - B ) - C$ and $Y = ( A - C ) - ( B - C ).$ Which one of the following is TRUE? $X = Y$ $X ⊂ Y$ $Y ⊂ X$ None of these
ritiksri8
commented
in
Set Theory & Algebra
Mar 17
by
ritiksri8
6.9k
views
gatecse-2005
set-theory&algebra
easy
set-theory
36
votes
6
answers
15
GATE CSE 2017 Set 2 | Question: 21
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
ritiksri8
answered
in
Set Theory & Algebra
Mar 17
by
ritiksri8
11.8k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
33
votes
8
answers
16
GATE IT 2008 | Question: 28
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only
ritiksri8
commented
in
Set Theory & Algebra
Mar 17
by
ritiksri8
15.0k
views
gateit-2008
set-theory&algebra
lattice
normal
24
votes
4
answers
17
GATE CSE 1997 | Question: 3.3
In the lattice defined by the Hasse diagram given in following figure, how many complements does the element ‘$e$’ have? $2$ $3$ $0$ $1$
ritiksri8
commented
in
Set Theory & Algebra
Mar 17
by
ritiksri8
7.5k
views
gate1997
set-theory&algebra
lattice
normal
2
votes
1
answer
18
Kenneth Rosen Edition 6th Exercise 1.1 Question 36 (Page No. 19)
What is the value of x after each of these statements is encountered in a computer program, if x = 1 before the statement is reached? if x + 2 = 3 then x := x + 1 if (x + 1 = 3) OR (2x + 2 = 3) then x := x + 1 if (2x + 3 = 5) AND (3x + 4 = 7) then x := x + 1 if (x + 1 = 2) XOR (x + 2 = 3) then x := x + 1 if x < 2 then x := x + 1
tbhaxor
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Mathematical Logic
Mar 16
by
tbhaxor
5.8k
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mathematical-logic
kenneth-rosen
discrete-mathematics
59
votes
7
answers
19
GATE CSE 2003 | Question: 32
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
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Mathematical Logic
Mar 15
by
꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂
16.9k
views
gatecse-2003
mathematical-logic
first-order-logic
normal
78
votes
6
answers
20
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂
comment edited
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Mathematical Logic
Mar 15
by
꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂
16.4k
views
gate1992
mathematical-logic
normal
first-order-logic
6
votes
3
answers
21
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 2
Which of the following expressions is false? $p \rightarrow q \equiv q \rightarrow p$ $\neg(p \vee q) \equiv \neg p \wedge \neg q$ $p \rightarrow q \equiv \neg q \rightarrow \neg p$ none of the above
i_m_sudip
answered
in
Mathematical Logic
Mar 15
by
i_m_sudip
333
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
1-mark
3
votes
2
answers
22
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 13
Let $p,q,r$ be three propositional variables. Which of the following statements is/are false? $p \rightarrow(q \vee r)) \equiv((p \wedge \neg q) \rightarrow r)$ $(p \wedge q) \vee r \equiv p \wedge(q \vee r)$ ... is FALSE then $(q \rightarrow p)$ is TRUE. If $(p \rightarrow q)$ is TRUE then $(q \rightarrow p)$ is FALSE.
i_m_sudip
answered
in
Mathematical Logic
Mar 15
by
i_m_sudip
364
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
23
votes
5
answers
23
GATE CSE 2023 | Question: 16
Geetha has a conjecture about integers, which is of the form \[ \forall x(P(x) \Longrightarrow \exists y Q(x, y)), \] where $P$ is a statement about integers, and $Q$ is a statement about pairs of integers. Which of the following (one or more) option(s) would imply ... $\exists y \forall x(P(x) \Longrightarrow Q(x, y))$ $\exists x(P(x) \wedge \exists y Q(x, y))$
ajayraho
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Mathematical Logic
Mar 14
by
ajayraho
11.0k
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gatecse-2023
mathematical-logic
first-order-logic
multiple-selects
1-mark
59
votes
6
answers
24
GATE CSE 2003 | Question: 37
Let \(f : A \to B\) be an injective (one-to-one) function. Define \(g : 2^A \to 2^B\) as: \(g(C) = \left \{f(x) \mid x \in C\right\} \), for all subsets $C$ of $A$. Define \(h : 2^B \to 2^A\) as: \(h(D) = \{x \mid x \in A, f(x) \in D\}\), for all ... always true? \(g(h(D)) \subseteq D\) \(g(h(D)) \supseteq D\) \(g(h(D)) \cap D = \phi\) \(g(h(D)) \cap (B - D) \ne \phi\)
shadymademe
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Set Theory & Algebra
Mar 14
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shadymademe
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gatecse-2003
set-theory&algebra
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difficult
0
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2
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25
Find no of sets A and B such that A n B = {3,5} and A U B = {2,3,5,7,8)
saisri
answer selected
in
Set Theory & Algebra
Mar 14
by
saisri
103
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34
votes
4
answers
26
GATE CSE 2005 | Question: 40
Let $P, Q,$ and $R$ be three atomic propositional assertions. Let $X$ denote $( P ∨ Q ) → R$ and $Y$ denote $(P → R) ∨ (Q → R).$ Which one of the following is a tautology? $X ≡ Y$ $X → Y$ $Y → X$ $¬Y → X$
i_m_sudip
answered
in
Mathematical Logic
Mar 13
by
i_m_sudip
6.5k
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gatecse-2005
mathematical-logic
propositional-logic
normal
0
votes
0
answers
27
UGC NET CSE | October 2022 | Part 1 | Question: 85
Consider $\alpha, \beta, \gamma$ as logical variables. Identify which of the following represents correct logical equivalence : (A) $(\alpha \wedge(\beta \vee \gamma)) \equiv((\alpha \wedge \beta) \vee(\alpha \wedge \gamma))$ ... options given below : (A) and (D) only (B) and (C) only, (A) and (C) only (B) and (D) only
Arjun
edited
in
Mathematical Logic
Mar 13
by
Arjun
188
views
ugcnetcse-oct2022-paper1
propositional-logic
0
votes
1
answer
28
Why inclusive or is used with Either...Or... here?
There are 2 propositions p: It is below freezing q: It is snowing. I want to write the symbolic form of: Either it is below freezing or it is snowing, but it is not snowing if it is freezing. This is what I came up with: ... . Second part it clear to me, but in the first shouldn't it will be exclusive or, because of Either...or...?
tbhaxor
commented
in
Mathematical Logic
Mar 13
by
tbhaxor
134
views
propositional-logic
9
votes
3
answers
29
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 6
Which of the following statements is true? The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2} \wedge \dots \wedge S_{n}\rightarrow S$ is satisfiable. The sentence $S$ is a logical ... $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is inconsistent.
ayushyadav05
commented
in
Mathematical Logic
Mar 13
by
ayushyadav05
866
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
1-mark
0
votes
1
answer
30
Does Either...Or means Exclusive Or or Inclusive Or?
Let's take a compound propositions Either it is below freezing or it is snowing. Now if $p$: it is below freezing $q$: it is snowing Will it be $p \vee q$ or $p \oplus q$? There are some instances where semantics are ... both cases can't be true, because if you are ill you can't appear for example and you must be in one state.
tbhaxor
answer selected
in
Mathematical Logic
Mar 13
by
tbhaxor
134
views
propositional-logic
mathematical-logic
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