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?
\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?
\exists x\left [P(x)\wedge \forall yQ(x,y) \right ] | |
\forall x \forall y Q(x,y) | |
\exists y \forall x \left [P(x) \Rightarrow Q(x,y) \right ] | |
\exists x \left [P(x) \wedge \exists y Q(x,y) \right ] |
Question 1 Explanation:
Question 2 |
The number of arrangements of six identical balls in three identical bins is ____.
7 | |
8 | |
12 | |
5 |
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]
S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))
[MSQ]
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 |
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?
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?
Both S1 and S2 are true. | |
S1 is true, but S2 is false. | |
S1 is false, but S2 is true. | |
Both S1 and S2 are false. |
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?
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?
Both S1 and S2 are tautologies. | |
S1 is a tautology but S2 is not a tautology | |
S1 is not a tautology but S2 is a tautology | |
Niether S1 nor S2 is a tautology |
Question 5 Explanation:
There are 5 questions to complete.
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 ” ∨”.
Thank You Intekhab Ahmad,
We have updated the answer.
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,
We have updated the answer.
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.
question 18 options given has a disjunction sign.
Thank You PRAFUL Rahul,
We have updated the question.
Question no. 34 none option is correct,
Thank You dp,
We have updated the option.
Please update the b and c options of 37th question
Thank You Mounika Dasa,
We have updated the option
In question 23 please update option c .
Thank You rajeev dubey,
We have updated the answer.
in Question 9 please update
F:∀x(∃yR(x,y))
in Question 9 please update
F:∀x(∃yR(x,y))
please check Que 50 on option c you put their or it need to change it and please correct them