search
Log In

Recent questions and answers in Mathematical Logic

54 votes
10 answers
1
In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell ... tail If the person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail
answered 1 day ago in Mathematical Logic Subhajit Panday 8.4k views
1 vote
1 answer
2
CONVERT IN TO LOGIC No one who loves some one is not loved by anyone lets S(x):x is somebody L(x,y):x loves y
answered 6 days ago in Mathematical Logic rish1602 97 views
0 votes
1 answer
3
18 votes
5 answers
4
$P$ and $Q$ are two propositions. Which of the following logical expressions are equivalent? $P ∨ \neg Q$ $\neg(\neg P ∧ Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ \neg Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ Q)$ Only I and II Only I, II and III Only I, II and IV All of I, II, III and IV
answered Jan 16 in Mathematical Logic Surya_Dev Chaturvedi 3.5k views
46 votes
4 answers
5
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown automaton. Let $\text{equivalent}$ be another predicate such that $\text{equivalent} (a,b)$ ...
answered Jan 16 in Mathematical Logic Surya_Dev Chaturvedi 6.6k views
1 vote
2 answers
6
if $\lambda$3 - 6$\lambda$2 -$\lambda$ +22=0 is a characteristic of 3 X 3 diagonal matrix , then trace of matrix A is
answered Jan 12 in Mathematical Logic Joey 622 views
0 votes
1 answer
8
1) IS P → Q ≡ Q → P Satisfiable Or NOT?
answered Jan 7 in Mathematical Logic eshita1997 91 views
0 votes
1 answer
9
Statements: Some boxes are triangles. All Spheres are triangles. All circles are boxes. All triangles are quadrilaterals. Conclusions: Some quadrilaterals are boxes. Some quadrilaterals are triangles. Some triangles are spheres. No circle is quadrilaterals. Options. 1 only 1st follow 2 only 1 ,2 ,3 follows 3 only 3rd follows 4 all follows
answered Jan 7 in Mathematical Logic eshita1997 160 views
0 votes
3 answers
10
14 votes
5 answers
11
What is logically equivalent to "If Kareena and Parineeti go to the shopping mall then it is raining": If Kareena and Parineeti do not go to the shopping mall then it is not raining. If Kareena and Parineeti do not go to the shopping mall then it is raining. If it ... go to the shopping mall. If it is not raining then Kareena and Parineeti do not go to the shopping mall. None of the above.
answered Jan 7 in Mathematical Logic eshita1997 956 views
18 votes
6 answers
12
Consider the following well-formed formulae: $\neg \forall x(P(x))$ $\neg \exists x(P(x))$ $\neg \exists x(\neg P(x))$ $\exists x(\neg P(x))$ Which of the above are equivalent? I and III I and IV II and III II and IV
answered Jan 7 in Mathematical Logic eshita1997 2.3k views
1 vote
3 answers
13
In a lottery, 10 tickets are drawn at random out of 50 tickets numbered from 1 to 50. What is the expected value of the sum of numbers on the drawn tickets?
answered Jan 7 in Mathematical Logic Joey 992 views
0 votes
1 answer
14
In a non-homogeneous equation Ax = b, x has a unique solution when $A^{-1}$ exists i.e x = $A^{-1}$b but when det(A) = 0 then we have infinite solution or many solution. please give a mathematical explanation of how the 2nd statement occurs?
answered Dec 31, 2020 in Mathematical Logic reboot 123 views
30 votes
11 answers
15
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ $( (p \to q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $
answered Dec 24, 2020 in Mathematical Logic Amcodes 5.6k views
1 vote
2 answers
17
2 votes
1 answer
18
Let the number of non-isomorphic groups of order 10 be X and number of non-isomorphic groups of order 24 be Y then the value of X and Y a) 3,2 b)2,7 c)1,7 d)4,5
answered Oct 11, 2020 in Mathematical Logic arun yadav 189 views
0 votes
1 answer
19
Consider the following first order logic statement $I)\forall x\forall yP\left ( x,y \right )$ $II)\forall x\exists yP\left ( x,y \right )$ $III)\exists x\exists yP\left ( x,y \right )$ $III)\exists x\forall yP\left ( x,y \right )$ ... $II)$ is true , then $III),IV)$ is true $B)$ If $IV)$ is true , then $II),III)$ is true $C)$ None of these
answered Oct 11, 2020 in Mathematical Logic arun yadav 200 views
0 votes
1 answer
20
The formula for the number of positive integers m which are less than p^k and relatively prime to p^k, where p is a prime number and k is a positive integer is__________- A)p^k(p-1) B)(p^(k-2))(p-1) C)p^k(p-2) D)(p^(k-1))(p-1)
answered Oct 8, 2020 in Mathematical Logic Krishnakumar Hatele 71 views
14 votes
2 answers
21
Three candidates, Amar, Birendra and Chanchal stand for the local election. Opinion polls are conducted and show that fraction $a$ of the voters prefer Amar to Birendra, fraction $b$ prefer Birendra to Chanchal and fraction $c$ ... $(a, b, c) = (0.49, 0.49, 0.49);$ None of the above.
answered Oct 4, 2020 in Mathematical Logic Amcodes 1.2k views
0 votes
3 answers
22
Which one is the correct translation of the following statement into mathematical logic? “None of my friends are perfect.” $\neg\:\exists\:x(p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land\neg\:q(x))$ $\exists\:x(p(x)\land\neg\:q(x))$
answered Sep 22, 2020 in Mathematical Logic Dhruvil 331 views
0 votes
1 answer
23
Some cat are intelligent express into first order logic if domain are animals
answered Sep 22, 2020 in Mathematical Logic Dhruvil 95 views
0 votes
1 answer
24
Consider the random variable X such that it takes values +1,-1 and +2 with probability 0.1 each .Calculate values of the commulative frequencydistribution function F(x) at x=-1 and x=1 and x=2 are ?
answered Sep 17, 2020 in Mathematical Logic arun yadav 98 views
21 votes
3 answers
25
0 votes
1 answer
26
Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively. If Z = max (X, Y), then the mean of Z is…. please explain in detail… https://gateoverflow.in/3676/gate2004-it-33 for min(X, Y) solution is already given as question asked in gate 2004. what about max(X, Y).
answered Sep 15, 2020 in Mathematical Logic arun yadav 60 views
28 votes
10 answers
27
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
answered Sep 13, 2020 in Mathematical Logic StoneHeart 9.5k views
4 votes
2 answers
28
Let $m$ and $n$ range over natural numbers and let $\text{Prime}(n)$ be true if $n$ is a prime number. Which of the following formulas expresses the fact that the set of prime numbers is infinite? $(\forall m) (\exists n) (n > m) \text{ implies Prime}(n)$ ... $(\exists n) (\forall m) (n > m) \wedge \text{Prime}(n)$
answered Sep 12, 2020 in Mathematical Logic indranil21 295 views
25 votes
2 answers
29
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is True Multiple Values False Cannot be determined
answered Sep 11, 2020 in Mathematical Logic Mitali gupta 4.3k views
11 votes
5 answers
30
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ $\exists x(p(x) \wedge W) \equiv \exists x \: p(x) \wedge W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
answered Sep 7, 2020 in Mathematical Logic Musa 4.5k views
0 votes
2 answers
31
Let $\{f_n(x)\}$ be a sequence of polynomials defined inductively as $f_1(x) = (x-2)^2$ $f_{n+1}(x) = (f_n(x)-2)^2, \qquad n\geq 1.$ Let $a_n$ and $b_n$ respectively denote the constant term and the coefficient of $x$ in $f_n(x).$ Then $a_n = 4, b_n = -4^n$ $a_n = 4, b_n = -4n^2$ $a_n = 4^{(n-1)!}, b_n = -4^n$ $a_n = 4^{(n-1)!}, b_n = -4n^2$
answered Sep 4, 2020 in Mathematical Logic `JEET 141 views
26 votes
6 answers
32
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 $P(x): x$ is precious $\forall x(P(x) \implies (G(x) \wedge S(x)))$ ... $\exists x((G(x) \wedge S(x)) \implies P(x))$ $\forall x((G(x) \vee S(x)) \implies P(x))$
answered Sep 4, 2020 in Mathematical Logic Musa 3.6k views
45 votes
4 answers
33
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 fool some person at some 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
answered Sep 3, 2020 in Mathematical Logic Musa 7.6k views
36 votes
7 answers
34
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
answered Sep 3, 2020 in Mathematical Logic Musa 6.5k views
21 votes
6 answers
35
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$ I only I and IV only II only II and III only
answered Sep 3, 2020 in Mathematical Logic Supriyo21 4.4k views
0 votes
1 answer
36
For each fo these statements find a domain for which the statements is true and a domain for which the statement is false. Everyone is studying discrete mathematics. Everyone is older than 21 years. Everyone two people have the same mother. No two different people have the same grandmother.
answered Sep 2, 2020 in Mathematical Logic Pawan Sharnagate 52 views
8 votes
3 answers
39
Show that the formula $\left[(\sim p \vee q) \Rightarrow (q \Rightarrow p)\right]$ is not a tautology. Let $A$ be a tautology and $B$ any other formula. Prove that $(A \vee B)$ is a tautology.
answered Aug 26, 2020 in Mathematical Logic subbus 858 views
0 votes
1 answer
40
Which of the following is FALSE? $Read\ \wedge as\ AND, \vee\ as\ OR, \sim as\ NOT, \rightarrow$ as one way implication and $\leftrightarrow$ as two way implication? $((x\rightarrow y)\wedge x)\rightarrow y$ $((\sim x\rightarrow y)\wedge (\sim x\wedge \sim y))\rightarrow x$ $(x\rightarrow (x\vee y))$ $((x\vee y)\leftrightarrow (\sim x\vee \sim y))$
asked Apr 2, 2020 in Mathematical Logic Lakshman Patel RJIT 117 views
To see more, click for all the questions in this category.
...