Recent questions and answers in Mathematical Logic

2 votes

3 answers

1

NIELIT 2017 July Scientist B (IT) - Section B: 13
Which of the following statements is false? $(P\land Q)\lor(\sim P\land Q)\lor(P \land \sim Q)$ is equal to $\sim Q\land \sim P$ $(P\land Q)\lor(\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor P$ ... $(P\land Q)\lor(\sim P\land Q)\lor (P \land \sim Q)$ is equal to $P\lor (Q\land \sim P)$

Mohitdas answered in Mathematical Logic Oct 11

314 views

7 votes

4 answers

2

GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$

Mohitdas answered in Mathematical Logic Oct 8

1.5k views

0 votes

1 answer

3

GATE ACADEMY TEST SERIES
What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?

raja11sep answered in Mathematical Logic Sep 26

89 views

0 votes

0 answers

4

Biconditional Operator in the logical expression for Symmetric Relation.
"The logical expression for the symmetric relation should contain the biconditional operator <-> instead of implication -> . Because, if u keep ->, then for the case when F -> T the ... " Could someone plz help, this seems to be correct. Also https://en.wikipedia.org/wiki/Symmetric_relation.

SHM asked in Mathematical Logic Sep 26

by SHM

28 views

0 votes

1 answer

5

Marks Distribution for Engineering and Discrete Maths
Hey all, As per brochure there will be 13 marks alloted for engineering maths. My quer is whether discrete maths will too be included in this 13 marks i.e. EM+DM=13, or Discrete maths will have separate marks? Like in Gate 2021 paper , the combined marks for Engineering and Discrete maths was over 13.

Arjun answered in Mathematical Logic Sep 12

by Arjun

66 views

2 votes

3 answers

6

UGCNET-Dec2015-II: 6
Which of the following arguments are not valid ? "If Gora gets the job and works hard, then he will be promoted. if Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard." "Either Puneet is not ... $n^2 > 1$, then $n>1$. a and c b and c a,b, and c a and b

forever_Learner answered in Mathematical Logic Aug 25

by forever_Learner

3.1k views

52 votes

5 answers

7

GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.

subbus answered in Mathematical Logic Aug 21

by subbus

7.8k views

2 votes

2 answers

8

Kenneth Rosen Edition 6th Exercise 1.1 Question 23 (Page No. 18)
State the converse, contrapositive, and inverse of each of these conditional statements. If it snows today, I will ski tomorrow. I come to class whenever there is going to be a quiz. A positive integer is a prime only if it has no divisors other than 1 and itself.

sabin324 answered in Mathematical Logic Aug 19

502 views

20 votes

6 answers

9

GATE CSE 2008 | Question: 31
$P$ 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

Renga98 answered in Mathematical Logic Aug 17

4.8k views

38 votes

3 answers

10

GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...

Renga98 answered in Mathematical Logic Aug 16

7.4k views

9 votes

2 answers

11

functions-combinations
Assume an almost injective function is a function in which exactly two element from domain maps to a single element in co-domain, otherwise function is injective. $S$ and $R$ are sets with cardinality $m$ and $n$ respectively. $(m<n)$ and $m\geq 2$. Number of almost injective ... $\frac{( n-m)!}{ 2}$ put m=2 and n=5. we get almost injective functions=5 shudnt it be C?

rish1602 answered in Mathematical Logic Aug 15

509 views

17 votes

5 answers

12

CMI2013-A-07
Consider the following two statements. There are infinitely many interesting whole numbers. There are finitely many uninteresting whole numbers. Which of the following is true? Statements $1$ and $2$ are equivalent. Statement $1$ implies statement $2$. Statement $2$ implies statement $1$. None of the above.

rish1602 answered in Mathematical Logic Aug 7

1.2k views

23 votes

3 answers

13

TIFR2012-A-3
Long ago,in a planet far far away, there lived three races of intelligent inhabitants: the blues (who always tell the truth), the whites (who always lie), and the pinks (who, when asked a series of questions, start with a lie and then tell the truth and lie alternately). To ... $C$ is Pink. $A$ is White, $B$ is Pink, $C$ is Blue. Cannot be determined from the above data.

rish1602 answered in Mathematical Logic Aug 4

1.5k views

30 votes

7 answers

14

GATE IT 2004 | Question: 31
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments: $P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$ $Q: [(¬p ∧q) ∧ [q → (p → r)]] → ¬r$ $R: [[(q ∧ r) → p] ∧ (¬q \vee p)] → r$ $S: [p ∧ (p → r) ∧ (q \vee ¬ r)] → q$ Which of the above arguments are valid? $P$ and $Q$ only $P$ and $R$ only $P$ and $S$ only $P, Q, R$ and $S$

Dharmesh Dubey answered in Mathematical Logic Aug 2

by Dharmesh Dubey

6.1k views

37 votes

6 answers

15

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

Dharmesh Dubey answered in Mathematical Logic Aug 2

by Dharmesh Dubey

6.3k views

30 votes

7 answers

16

GATE CSE 2007 | Question: 22
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ ... $\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$

rish1602 answered in Mathematical Logic Jul 25

5.6k views

1 vote

1 answer

17

Zeal Test Series 2019: Mathematical Logic - Propositional Logic
Isn’t the 3) statement is wrong it should be [(p->r)^(q->r)]->[(p∨q)->r] \

rish1602 answered in Mathematical Logic Jul 19

246 views

3 votes

2 answers

18

Proposition
Consider the following set of propositions 1. I carry an umbrella only if it rains. 2. If I carry an umbrella I use it. 3. I get wet in rain only if I don't use umbrella. 4. It rains today. Possible Conclusion is: A. I will not get wet today. B. I will get wet today. C. I might get wet today. D. None of the above.

rish1602 answered in Mathematical Logic Jul 18

499 views

57 votes

4 answers

19

GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$

rish1602 answered in Mathematical Logic Jul 18

10.1k views

17 votes

6 answers

20

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 $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$

rish1602 answered in Mathematical Logic Jul 18

6.7k views

0 votes

2 answers

21

#Basic #DiscreteMathematics #KennethRosen
Suppose that there are 9 faculty members in the mathematics department and 11 in the computer science department. How many ways are there to select a committee to develop a discrete mathematics course at a school if the committee is to consist of ... use Sum rule. How to decide on Product rule or Sum rule? Please use some basic example for both the cases.

AdityaYadav answered in Mathematical Logic Jul 16

1.6k views

37 votes

8 answers

22

GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$

aryavart answered in Mathematical Logic Jul 15

7.2k views

16 votes

3 answers

23

TIFR2013-A-3
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.

subbus answered in Mathematical Logic May 24

by subbus

1.5k views

19 votes

3 answers

24

TIFR2011-A-12
The action for this problem takes place in an island of Knights and Knaves, where Knights always make true statements and Knaves always make false statements and everybody is either a Knight or a Knave. Two friends A and B lives in a house. The census taker (an outsider) ... B is a Knave. A is a Knave and B is a Knight. Both are Knaves. Both are Knights. No conclusion can be drawn.

subbus answered in Mathematical Logic May 16

by subbus

1.1k views

19 votes

5 answers

25

TIFR2011-A-1
If either wages or prices are raised, there will be inflation. If there is inflation, then either the government must regulate it or the people will suffer. If the people suffer, the government will be unpopular. Government will not be unpopular. Which of the ... are not raised Prices are not raised If the inflation is not regulated, then the prices are not raised Wages are not raised

subbus answered in Mathematical Logic May 16

by subbus

1.7k views

63 votes

11 answers

26

GATE CSE 2015 Set 3 | Question: 24
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 ... person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail

subbus answered in Mathematical Logic May 16

by subbus

10.3k views

1 vote

3 answers

27

NIELIT 2017 July Scientist B (CS) - Section B: 16
Which of the following propositions is tautology? $(p\lor q)\to q$ $p\lor (q\to p)$ $p\lor (p\to q)$ Both (B) and (C)

Hira Thakur answered in Mathematical Logic May 13

345 views

7 votes

2 answers

28

CMI2015-A-01
Twin primes are pairs of numbers $p$ and $p+2$ such that both are primes-for instance, $5$ and $7$, $11$ and $13$, $41$ and $43$. The Twin Prime Conjecture says that there are infinitely many twin primes. Let $\text{TwinPrime}(n)$ ... $\exists m \cdot \forall n \cdot \text{TwinPrime}(n) \text{ implies }n \leq m$

soujanyareddy13 answered in Mathematical Logic May 6

by soujanyareddy13

589 views

2 votes

2 answers

29

CMI2019-B-5
In the land of Twitter, there are two kinds of people: knights (also called outragers), who always tell the truth, and knaves (also called trolls), who always lie. It so happened that a person with handle @anand tweeted something offensive. It was not known ... $3:$ My lawyer always tells the truth. Which of the above suspects are innocent, and which are guilty? Explain your reasoning.

soujanyareddy13 answered in Mathematical Logic May 4

by soujanyareddy13

308 views

63 votes

4 answers

30

GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$

Deepakk Poonia (Dee) answered in Mathematical Logic Apr 14

by Deepakk Poonia (Dee)

11.4k views

70 votes

6 answers

31

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 ___________.

subbus answered in Mathematical Logic Apr 12

by subbus

11.9k views

39 votes

4 answers

32

GATE CSE 2014 Set 3 | Question: 1
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? Only L is TRUE. Only M is TRUE. Only N is TRUE. L, M and N are TRUE.

subbus answered in Mathematical Logic Apr 12

by subbus

6.7k views

24 votes

3 answers

33

GATE CSE 2004 | Question: 70
The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not valid valid a contradiction None of the above

subbus answered in Mathematical Logic Apr 2

by subbus

4.4k views

20 votes

8 answers

34

GATE CSE 1996 | Question: 2.3
Which of the following is NOT True? (Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication) $((x \rightarrow y) \wedge x) \rightarrow y$ ... $(x \rightarrow (x \vee y))$ $((x \vee y) \leftrightarrow (\neg x \rightarrow \neg y))$

subbus answered in Mathematical Logic Mar 25

by subbus

4.9k views

32 votes

3 answers

35

GATE CSE 1995 | Question: 2.19
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

subbus answered in Mathematical Logic Mar 25

by subbus

5.6k views

43 votes

5 answers

36

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) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$

tirth_patel answered in Mathematical Logic Mar 5

11.4k views

1 vote

2 answers

37

logic basic
Let P(x) , Q(x) and R(x) be the statements "x is a clear explantion " , "x is satisfactory " and "x is an excuse " resp Suppose that the domain x consists of all English text Express each of these using ... All clear explanation are satisfactory 2) Some excuses are unsatisfactory 3) Some excuses are not clear explanation 4) does 3 follow from 1and 2

ijnuhb answered in Mathematical Logic Mar 3

by ijnuhb

177 views

25 votes

5 answers

38

GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above

subbus answered in Mathematical Logic Mar 2

by subbus

4.4k views

23 votes

5 answers

39

GATE CSE 1990 | Question: 3-x
Indicate which of the following well-formed formulae are valid: $\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)$ ...

subbus answered in Mathematical Logic Feb 28

by subbus

4.8k views

14 votes

6 answers

40

GATE CSE 1989 | Question: 3-v
Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$

subbus answered in Mathematical Logic Feb 28

by subbus

1.8k views

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