Recent questions tagged goclasses_2025_cs_dm_tw

5 votes

3 answers

1

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 1
For a given predicate $\mathrm{P}(\mathrm{x}),$ you might believe that the statements $\forall \mathrm{xP}(\mathrm{x})$ or $\exists \mathrm{xP}(\mathrm{x})$ ... the domain, that $P(n)$ is true. Show for every element $n$ in the domain, that $P(n)$ is false.

For a given predicate $\mathrm{P}(\mathrm{x}),$ you might believe that the statements $\forall \mathrm{xP}(\mathrm{x})$ or $\exists \mathrm{xP}(\mathrm{x})$ are either tr...

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GO Classes asked Apr 18, 2023

6 votes

3 answers

2

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 5
Consider the statement $\text{S} :$ "For all natural numbers $n,$ if $n$ is prime, then $n$ is antisocial." You do not need to know what antisocial means for this problem, just that it is a property ... $10$ is antisocial. $10$ is not antisocial. $7$ is antisocial. $7$ is not antisocial.

Consider the statement $\text{S} :$ "For all natural numbers $n,$ if $n$ is prime, then $n$ is antisocial."You do not need to know what antisocial means for this problem,...

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GO Classes asked Apr 18, 2023

7 votes

2 answers

3

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 6
Suppose $P(x, y)$ is some binary predicate defined on a very small domain of discourse: just the integers $1,2,3$, and $4.$ For each of the $16$ pairs of these numbers, $P(x, y)$ is either true or false, according to the following ... $\exists x \forall y P(x, y)$. $\exists y \forall x P(x, y)$.

Suppose $P(x, y)$ is some binary predicate defined on a very small domain of discourse: just the integers $1,2,3$, and $4.$ For each of the $16$ pairs of these numbers, $...

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GO Classes asked Apr 18, 2023

12 votes

2 answers

4

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 7
Let $P(x)$ and $Q(x)$ be predicates and let $D$ denote the domain of the predicate variable $x$. Consider the following universal conditional statement, $ \forall x \in D, P(x) \rightarrow Q(x) . $ Which of the following conditions ... is true for all $x \in D$. $P(x) \vee Q(x)$ is true for all $x \in D$.

Let $P(x)$ and $Q(x)$ be predicates and let $D$ denote the domain of the predicate variable $x$. Consider the following universal conditional statement,$$\forall x \in D,...

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GO Classes asked Apr 18, 2023

6 votes

1 answer

5

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 8
Let $P(x), Q(x), R(x)$ and $S(x)$ denote the following predicates with domain $\mathbb{Z}$ ... $\forall x \in \mathbb{Z}, \quad S(x) \rightarrow(Q(x) \wedge S(x))$

Let $P(x), Q(x), R(x)$ and $S(x)$ denote the following predicates with domain $\mathbb{Z}$ :$$\begin{aligned}& P(x): x^2-x-12=0, \\& Q(x): x \text { is odd, } \\& R(x): x...

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340 views

GO Classes asked Apr 18, 2023

9 votes

2 answers

6

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 15
Let's make a trip to a new world called "Never Never Land". Regular, ordinary first-order logic has two quantifiers: $\forall$ and $\exists$. Now, let's imagine we lived in a world in which these quantifiers ... $\mathrm{Nx}(\neg A(x) \wedge B(x))$

Let's make a trip to a new world called "Never Never Land".Regular, ordinary first-order logic has two quantifiers: $\forall$ and $\exists$.Now, let's imagine we lived in...

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500 views

GO Classes asked Apr 18, 2023

9 votes

1 answer

7

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1| Question: 10
Which of the following formulas is a formalization of the sentence : There is a barber who shaves all men in the town who do not shave themselves Where $\text{shave}(x,y)$ means $x\;\text{shaves}\; y$ ...

Which of the following formulas is a formalization of the sentence :“There is a barber who shaves all men in the town who do not shave themselves”Where $\text{shave}(...

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505 views

GO Classes asked Apr 14, 2022

12 votes

1 answer

8

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1| Question: 12
We define a new quantifier, uniqueness quantifier, the symbol of which is $\exists!.$ For any predicate $\text{P}$ and universe $\text{U}, \exists! x \text{P}(x)$ ... I, II, IV I, III II, III, IV IV only

We define a new quantifier, uniqueness quantifier, the symbol of which is $\exists!.$For any predicate $\text{P}$ and universe $\text{U}, \exists! x \text{P}(x)$ means th...

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GO Classes asked Apr 14, 2022

13 votes

2 answers

9

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 11
Translate the following sentences into First-order logic (FOL): If someone is noisy, everybody is annoyed. Use the following predicates : $\text{N}(x)\;:$ $x$ is noisy $\text{A}(x)\;:$ $x$ is annoyed Which of the ... $\forall x(\text{N}(x) \rightarrow \forall y(\text{A}(y)))$

Translate the following sentences into First-order logic (FOL): “ If someone is noisy, everybody is annoyed.”Use the following predicates :$\text{N}(x)\;:$ “$x$ is ...

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GO Classes asked Apr 14, 2022

10 votes

2 answers

10

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 14
Let $\text{P}$ be a compound proposition over $4$ propositional variables $: a,b,c,d.$ We know that for a compound proposition over n propositional variables, we have $2^{n}$ rows in the truth table. Every row of the ... the sentence $(a \wedge b) \vee (b \wedge c)$ How many models are there for $\text{P}?$

Let $\text{P}$ be a compound proposition over $4$ propositional variables $: a,b,c,d.$We know that for a compound proposition over n propositional variables, we have $2^{...

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663 views

GO Classes asked Apr 14, 2022

10 votes

2 answers

11

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 3
Which of the following is the negation of “there is a successful person who is grateful”? There is a successful person who is ungrateful. Every grateful person is unsuccessful. Every unsuccessful person is grateful. Every successful person is ungrateful.

Which of the following is the negation of “there is a successful person who is grateful”?There is a successful person who is ungrateful.Every grateful person is unsuc...

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673 views

GO Classes asked Apr 14, 2022

14 votes

2 answers

12

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 9
Many programming languages support a ternary conditional operator. For example, in $\text{C, C++},$ and $\text{Java}$, the expression $x ? y : z$ means evaluate the boolean expression $x.$ If it's true, the entire expression ... $p ? p : (\neg p)$ is tautology. $(\neg p) ? p : (\neg p)$ is tautology.

Many programming languages support a ternary conditional operator. For example, in $\text{C, C++},$ and $\text{Java}$, the expression $x ? y : z$ means “evaluate the bo...

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545 views

GO Classes asked Apr 14, 2022

9 votes

1 answer

13

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 13
Consider the following predicates. $\text{Rabbit}(x) = x$ is a rabbit. $\text{Cute}(x) = x$ is cute. Consider the following statement $\text{E},$ where the domain of every variable is set of all animals in a ... no cute rabbit in jungle $\text{J}.$ There is some rabbit who is not cute in jungle $\text{J}.$

Consider the following predicates.$\text{Rabbit}(x) = x$ is a rabbit.$\text{Cute}(x) = x$ is cute.Consider the following statement $\text{E},$ where the domain of every v...

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588 views

GO Classes asked Apr 14, 2022

7 votes

2 answers

14

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 4
Consider the following predicates. $\text{Rabbit}(x) = x$ is a rabbit. $\text{Cute}(x) = x$ is cute. Consider the following statement $\text{E},$ ... $\text{J}.$

Consider the following predicates.$\text{Rabbit}(x) = x$ is a rabbit.$\text{Cute}(x) = x$ is cute.Consider the following statement $\text{E},$ where the domain of every v...

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616 views

GO Classes asked Apr 14, 2022

15 votes

2 answers

15

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 2
Consider the following proposition : $\text{A}_{n} = \underbrace{(p \rightarrow (q \rightarrow (p \rightarrow (q \rightarrow (\dots)))))}_{\text{number of p's + number of q's = n}}.$ Which of the following is false for ... $n > 2, \text{A}_{n}$ is Not contingency.

Consider the following proposition :$\text{A}_{n} = \underbrace{(p \rightarrow (q \rightarrow (p \rightarrow (q \rightarrow (\dots)))))}_{\text{number of p’s + number o...

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GO Classes asked Apr 14, 2022

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