Propositional Logic

 Question 1
Geetha has a conjecture about integers, which is of the form
$\forall x\left [P(x)\Rightarrow \exists yQ(x,y) \right ]$
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 Geetha's conjecture?
 A $\exists x\left [P(x)\wedge \forall yQ(x,y) \right ]$ B $\forall x \forall y Q(x,y)$ C $\exists y \forall x \left [P(x) \Rightarrow Q(x,y) \right ]$ D $\exists x \left [P(x) \wedge \exists y Q(x,y) \right ]$
GATE CSE 2023   Discrete Mathematics
Question 1 Explanation:
 Question 2
The number of arrangements of six identical balls in three identical bins is ____.
 A 7 B 8 C 12 D 5
GATE CSE 2022   Discrete Mathematics
Question 2 Explanation:

 Question 3
Choose the correct choice(s) regarding the following proportional logic assertion S:

$S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$
[MSQ]
 A S is neither a tautology nor a contradiction B S is a tautology C S is a contradiction D The antecedent of S is logically equivalent to the consequent of S
GATE CSE 2021 SET-2   Discrete Mathematics
Question 3 Explanation:
 Question 4
Consider the two statements.

S1: There exist random variables $X$ and $Y$ such that $\left(\mathbb E[(X-\mathbb E(X))(Y-\mathbb E(Y))]\right)^2 > \textsf{Var}[X]\textsf{Var}[Y]$
S2: For all random variables $X$ and $Y$, $\textsf{Cov}[X,Y]=\mathbb E \left[|X-\mathbb E[X]||Y-\mathbb E[Y]|\right ]$

Which one of the following choices is correct?
 A Both S1 and S2 are true. B S1 is true, but S2 is false. C S1 is false, but S2 is true. D Both S1 and S2 are false.
GATE CSE 2021 SET-1   Discrete Mathematics
Question 4 Explanation:
 Question 5
Let p and q be two propositions. Consider the following two formulae in propositional logic.

$S1: (\neg p\wedge(p\vee q))\rightarrow q$
$S2: q\rightarrow(\neg p\wedge(p\vee q))$

Which one of the following choices is correct?
 A Both S1 and S2 are tautologies. B S1 is a tautology but S2 is not a tautology C S1 is not a tautology but S2 is a tautology D Niether S1 nor S2 is a tautology
GATE CSE 2021 SET-1   Discrete Mathematics
Question 5 Explanation:

There are 5 questions to complete.

18 thoughts on “Propositional Logic”

1. Qno. 40. Correction in option 4
The actual option is ∀x [(tiger(x) ∨ lion(x)) → (hungry(x) ∨ threatened(x)) → attacks(x)]
At the place of “∧ , there will be ” ∨”.

2. In the question 23 please update the answer. It is not 0, instead it needs to be ∀x(∃y(¬α)→∃z(¬β))

• Thank You MOUNIKA DASA,

3. In the question 29 please update the question. In the option iv it is not ¬∃x(¬P(x)), instead it needs to be ∃x(¬P(x))

• Thank You MOUNIKA DASA,
We have updated the question.

4. question 18 options given has a disjunction sign.

• Thank You PRAFUL Rahul,
We have updated the question.

5. Question no. 34 none option is correct,

• Thank You dp,
We have updated the option.

6. Please update the b and c options of 37th question

• Thank You Mounika Dasa,
We have updated the option

7. In question 23 please update option c .

• Thank You rajeev dubey,

8. in Question 9 please update
F:∀x(∃yR(x,y))