1

GATE CSE 2021 Set 1

MCQ (More than One Correct Answer)

+2

-0.67

A relation R is said to be circular if a

**R**b and b**R**c together imply c**R**a. Which of the following options is/are correct?2

GATE CSE 2019

MCQ (Single Correct Answer)

+2

-0.67

Consider the first order predicate formula φ:

∀x[(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (z = 1)))]

Here 'a|b' denotes that 'a divides b', where a and b are integers.

Consider the following sets:

S1. {1, 2, 3, ..., 100}

S2. Set of all positive integers

S3. Set of all integers

Which of the above sets satisfy φ?

∀x[(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (z = 1)))]

Here 'a|b' denotes that 'a divides b', where a and b are integers.

Consider the following sets:

S1. {1, 2, 3, ..., 100}

S2. Set of all positive integers

S3. Set of all integers

Which of the above sets satisfy φ?

3

GATE CSE 2018

MCQ (Single Correct Answer)

+2

-0.6

Let N be the set of natural numbers. Consider the following sets.

$$\,\,\,\,\,\,\,\,$$ $$P:$$ Set of Rational numbers (positive and negative)

$$\,\,\,\,\,\,\,\,$$ $$Q:$$ Set of functions from $$\left\{ {0,1} \right\}$$ to $$N$$

$$\,\,\,\,\,\,\,\,$$ $$R:$$ Set of functions from $$N$$ to $$\left\{ {0,1} \right\}$$

$$\,\,\,\,\,\,\,\,$$ $$S:$$ Set of finite subsets of $$N.$$

Which of the sets above are countable?

4

GATE CSE 2016 Set 2

MCQ (Single Correct Answer)

+2

-0.6

A binary relation $$R$$ on $$N \times N$$ is defined as follows: $$(a,b)R(c,d)$$ if $$a \le c$$ or $$b \le d.$$ Consider the following propositions:

$$P:$$ $$R$$ is reflexive

$$Q:$$ $$R$$ is transitive

Which one of the following statements is **TRUE**?

Questions Asked from Set Theory & Algebra (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2024 Set 2 (1)
GATE CSE 2024 Set 1 (1)
GATE CSE 2023 (1)
GATE CSE 2021 Set 1 (1)
GATE CSE 2019 (1)
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GATE CSE 2016 Set 2 (2)
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GATE CSE 2015 Set 3 (1)
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GATE CSE 1998 (3)
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GATE CSE 1995 (1)
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GATE CSE 1989 (1)
GATE CSE 1988 (1)

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