# Set Theory

 Question 1
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?
 A $H$ is a group. B Every element in $H$ has an inverse, but $H$ is NOT a group. C For every $A \in 2^X$, the inverse of $A$ is the complement of $A$. D For every $A \in 2^X$, the inverse of $A$ is $A$.
GATE CSE 2023   Discrete Mathematics
Question 1 Explanation:
 Question 2
Let S be a set of consisting of 10 elements. The number of tuples of the form (A,B) such that A and B are subsets of S, and $A\subseteq B$ is _______
 A 49049 B 59049 C 3524 D 854
GATE CSE 2021 SET-2   Discrete Mathematics
Question 2 Explanation:

 Question 3
If $A=\{x, y, z\}$ and $B=\{u, v, w, x\}$, and the universe is $\{s, t, u, v, w, x, y, z\}$. Then $(A \cup \bar{B}) \cap(A \cap B)$ is equal to
 A $\{u,v,w,x\}$ B $\{x\}$ C $\{u,v,w,x,y,z\}$ D $\{u,v,w\}$
ISRO CSE 2020   Discrete Mathematics
Question 3 Explanation:
NOTE: This question is Excluded for evaluation. Originally all Options are wrong. We have modified one option.

 Question 4
Consider the first order predicate formula:
$\forall x[\forall z\; z|x\Rightarrow ((z=x)\vee (z=1))\Rightarrow$ $\exists w(w> x)\wedge (\forall z \; z|w\Rightarrow ((w=z)\vee (z=1)))]$
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 $\varphi$ ?
 A S1 and S2 B S1 and S3 C S2 and S3 D S1,S2 and S3
GATE CSE 2019   Discrete Mathematics
Question 4 Explanation:
 Question 5
Let $U=\{1,2,,...n\}$. Let $A=\{(x,X)|x\in X,X\subseteq U\}$. Consider the following two statements on |A|.

I. $|A|=n2^{n-1}$
II. $|A|=\sum_{k=1}^{n}k\binom{n}{k}$

Which of the above statements is/are TRUE?
 A Only I B Only II C Both I and II D Neither I nor II
GATE CSE 2019   Discrete Mathematics
Question 5 Explanation:

There are 5 questions to complete.

### 7 thoughts on “Set Theory”

1. There was an error in the question no 6, please update the option(d) to P, Q and S.

• Thank You MOUNIKA DASA,
We have updated the option.

2. There is an error in question 40 in the last option it is ” S does not belong to Power set”