# Set Theory

 Question 1
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 1 Explanation:
 Question 2
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 2 Explanation:
NOTE: This question is Excluded for evaluation. Originally all Options are wrong. We have modified one option.

Click here for detail solution by gateoverflow
 Question 3
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 3 Explanation:
 Question 4
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 4 Explanation:
 Question 5
The following paradigm can be used to find the solution of the problem in minimum time:
Given a set of non-negative integer and a value K, determine if there is a subset of the given set with sum equal to K:
 A Divide and Conquer B Dynamic Programming C Greedy Algorithm D Branch and Bound
ISRO CSE 2018   Discrete Mathematics
Question 5 Explanation:
 Question 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 {0, 1} to N
R: Set of functions from N to {0, 1}
S: Set of finite subsets of N.
Which of the sets above are countable?
 A Q and S only B P and S only C P and R only D P, Q and S only
GATE CSE 2018   Discrete Mathematics
Question 6 Explanation:
 Question 7
The symmetric difference of sets A={1,2,3,4,5,6,7,8} and B={1,3,5,6,7,8,9} is:
 A {1,3,5,6,7,8} B {2,4,9} C {2,4} D {1,2,3,4,5,6,7,8,9}
ISRO CSE 2017   Discrete Mathematics
Question 7 Explanation:
 Question 8
Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following statements:

I. Each compound in U \ S reacts with an odd number of compounds.
II. At least one compound in U \ S reacts with an odd number of compounds.
III. Each compound in U n S reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?
 A Only I B Only II C Only III D None
GATE CSE 2016 SET-2   Discrete Mathematics
Question 8 Explanation:
 Question 9
A function $f:\mathbb{N}^{+}\rightarrow \mathbb{N}^{+}$, defined on the set of positive integers $\mathbb{N}^{+}$, satisfies the following properties:
f(n)=f(n/2) if n is even
f(n)=f(n+5) if n is odd
Let R={$i|\exists j:f(j)=i$} be the set of distinct values that f takes. The maximum possible size of R is ____.
 A 1 B 2 C 3 D 4
GATE CSE 2016 SET-1   Discrete Mathematics
Question 9 Explanation:
 Question 10
Suppose U is the power set of the set S={1,2,3,4,5,6}. For any T$\in$U, let |T| denote the number of elements in T and T' denote the complement of T. For any T,R$\in$U, let T\R be the set of all elements in T which are not in R. Which one of the following is true?
 A $\forall X\in U \; (|X|=|X'|)$ B $\exists X\in U \; \exists Y\in U \;$ $(|X|=2,\; |Y|=3 \; and \; X \setminus Y=\phi )$ C $\forall X\in U \; \forall Y\in U \;$ $(|X|=5,\; |Y|=5 \; and \; X \cap Y=\phi )$ D $\forall X \in U \; \forall Y\in U\; (X \setminus Y=Y' \setminus X')$
GATE CSE 2015 SET-3   Discrete Mathematics
Question 10 Explanation:
There are 10 questions to complete.

### 4 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. • 