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))

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

Please check the option B of the Question 23

It should be ((a→c)→(~b→(a^c))