1

GATE CSE 2023

MCQ (More than One Correct Answer)

+2

-0.67

Let $$f:A \to B$$ be an onto (or surjective) function, where A and B are nonempty sets. Define an equivalence relation $$\sim$$ on the set A as

$${a_1} \sim {a_2}$$ if $$f({a_1}) = f({a_2})$$,

where $${a_1},{a_2} \in A$$. Let $$\varepsilon = \{ [x]:x \in A\} $$ be the set of all the equivalence classes under $$\sim$$. Define a new mapping $$F:\varepsilon \to B$$ as

$$F([x]) = f(x)$$, for all the equivalence classes $$[x]$$ in $$\varepsilon $$.

Which of the following statements is/are TRUE?

2

GATE CSE 2023

MCQ (More than One Correct Answer)

+2

-0.67

Let X be a set and 2$$^X$$ denote the powerset of X. Define a binary operation $$\Delta$$ on 2$$^X$$ as follows:

$$A\Delta B=(A-B)\cup(B-A)$$.

Let $$H=(2^X,\Delta)$$. Which of the following statements about H is/are correct?

3

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?4

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?

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 (2)
GATE CSE 2021 Set 1 (1)
GATE CSE 2019 (1)
GATE CSE 2018 (1)
GATE CSE 2016 Set 2 (2)
GATE CSE 2016 Set 1 (1)
GATE CSE 2015 Set 3 (1)
GATE CSE 2015 Set 2 (2)
GATE CSE 2014 Set 2 (1)
GATE CSE 2014 Set 3 (2)
GATE CSE 2014 Set 1 (1)
GATE CSE 2012 (1)
GATE CSE 2009 (1)
GATE CSE 2007 (4)
GATE CSE 2006 (4)
GATE CSE 2005 (3)
GATE CSE 2004 (2)
GATE CSE 2002 (1)
GATE CSE 2001 (2)
GATE CSE 2000 (2)
GATE CSE 1999 (1)
GATE CSE 1998 (3)
GATE CSE 1996 (3)
GATE CSE 1995 (1)
GATE CSE 1994 (1)
GATE CSE 1989 (1)
GATE CSE 1988 (1)

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