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GATE preparation for Computer Science & Information Technology

(309 Posts)

This thread is dedicated to preparation for Computer Science & Information Technology - CS section of GATE. You may share questions from topics like Engineering Mathematics, Programming - C / C++, Network Security and Firewall, Java Basics, Digital Logic, Computer Organization and Architecture, Programming and Data Structure, Algorithms, Theory of Computation, Compiler Design, Operating System, Databases, Information Systems and Software, Computer Networks, Web Technologies etc.

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Bhanu Pratap Singh Rathore
Shared from GATE-2018 (CS) on 26 Jun, 2019 4:08 PM

Consider the first-order logic sentence

Where is a quantifier-free first-order logic formula using only predicate
symbols and possibly equality, but no function symbols. Suppose has a model with a universe
containing 7 elements.

Which one of the following statements is necessarily true?

 
There exists at least one model of with universe of size less than or equal to 3.
There exists no model of with universe of size less than or equal to 3.
There exists no model of with universe of size greater than 7.
Every model of has a universe of size equal to 7.
Please type your answer before submitting.
Bhanu Pratap Singh Rathore
Posted on 26 Jun, 2019 4:08 PM

Let's interpret the problem this way : ∀ are always True and ∃ are always False for empty sets. So there exists at least one model with universe of size 3 (or less than). Therefore, option (A) is necessarily TRUE.

Bhanu Pratap Singh Rathore
Shared from GATE-2018 (CS) on 25 Jun, 2019 6:08 PM

Let N be the set of natural number

Consider the following sets
P: Set of Rational numbers (positive and negative)
Q: Set of functions from {0, 1} to N
R: Set of functions from N to {0, 1}
S: Set of finite subset of N.

Which of the sets above are countable?

 
Q and S only
P and S only
P and R only
P, Q and S only
Please type your answer before submitting.
Bhanu Pratap Singh Rathore
Posted on 25 Jun, 2019 6:08 PM

If a set S is countable, then P(S) i.e 2^S is uncountable.

Bhanu Pratap Singh Rathore
Shared from GATE-2018 (CS) on 25 Jun, 2019 4:33 PM

Consider the relations r(A, B) ands (B, C), where s.B is a primary key and r.B is a foreign key referencing s. B. Consider the query
Q : r

Let LOJ denote the natural left outer-join operation. Assume that r and s contain no null values. Which one of the following queries is NOT equivalent to Q?

 
(r s)
(rLOJs)
rLOJ
(r)LOJs
Please type your answer before submitting.
Bhanu Pratap Singh Rathore
Posted on 25 Jun, 2019 4:33 PM

There is some mistake in question. Consider the relations r(A, B) and s(B, C), where s.B is a primary key and r.B is a foreign key referencing s.B. Consider the query Q: r⋈(σB<5(s)) Let LOJ denote the natural left outer-join operation. Assume that r and s contain no null values. Which one of the following is NOT equivalent to Q? (A) σB<5(r ⋈ s) (B) σB<5(r LOJ s) (C) r LOJ (σB<5(s)) (D) σB<5(r)LOJ s

Sumit Lahiri
Shared from GATE-2010 (CS) on 18 Jan, 2019 3:28 PM

Consider the following languages.



Which of these languages is/are regular?

 
Only L1 and L2
Only L3 and L4
Only L2, L3 and L4
Only L3
Please type your answer before submitting.
Sumit Lahiri
Posted on 18 Jan, 2019 3:28 PM

How come L4 is regular?????????. Please explain. A Turing machine case be used to recognize it with infinite tape.

Sumit Lahiri
Shared from GATE-2016 (CS) Set-I on 06 Jan, 2019 8:29 AM

Let X be a recursive language and Y be a recursively enumerable but not recursive language.
Let W and Z be two languages such that Y reduces to W, and Z reduces to X (reduction means the standard many-one reduction). Which one of the following statements is TRUE?

 
W can be recursively enumerable and Z is recursive.
W can be recursive and Z is recursively enumerable.
W is not recursively enumerable and Z is recursive.
W is not recursively enumerable and Z is not recursive.
Na
Please type your answer before submitting.
Sumit Lahiri
Posted on 06 Jan, 2019 8:30 AM

Https://gateoverflow.in/39721/gate2016-1-44