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Recent questions tagged sets

0 votes
1 answer
1
If $S$ be an infinite set and $S​_1​\dots\dots ,S​_n​$ be sets such that $S​_1 ​\cup S​_2​ \cup \dots \cup S​_n​ =S$, then at least one of the set $S​_i$​ is a finite set. not more than one of the sets $S​_i​$ can be finite. at least one of the sets $S​_i​$ is an infinite set. not more than one of the sets $S​_i​$ can be infinite.
asked Mar 31, 2020 in Set Theory & Algebra Lakshman Patel RJIT 131 views
1 vote
1 answer
5
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-one For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.
asked Feb 17, 2020 in Set Theory & Algebra vivek_mishra 307 views
2 votes
1 answer
6
If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$. Then $(A \cup \overline{B}) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ \: \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$
asked Jan 13, 2020 in Set Theory & Algebra Satbir 359 views
1 vote
1 answer
7
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1\} \:\:\:\:\:\:\: B=\{(x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is non-empty none of the above
asked Sep 23, 2019 in Set Theory & Algebra Arjun 277 views
2 votes
1 answer
8
Let $\mathbb{N}=\{1,2,3, \dots\}$ be the set of natural numbers. For each $n \in \mathbb{N}$, define $A_n=\{(n+1)k, \: k \in \mathbb{N} \}$. Then $A_1 \cap A_2$ equals $A_3$ $A_4$ $A_5$ $A_6$
asked Sep 23, 2019 in Set Theory & Algebra Arjun 141 views
1 vote
2 answers
9
Let $A$ and $B$ be disjoint sets containing $m$ and $n$ elements respectively, and let $C=A \cup B$. Then the number of subsets $S$ (of $C$) which contains $p$ elements and also has the property that $S \cap A$ contains $q$ ... $\begin{pmatrix} m \\ p-q \end{pmatrix} \times \begin{pmatrix} n \\ q \end{pmatrix}$
asked Sep 23, 2019 in Set Theory & Algebra Arjun 253 views
1 vote
2 answers
10
A set contains $2n+1$ elements. The number of subsets of the set which contain at most $n$ elements is $2^n$ $2^{n+1}$ $2^{n-1}$ $2^{2n}$
asked Sep 23, 2019 in Set Theory & Algebra Arjun 229 views
1 vote
2 answers
11
Let $X$ be the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$. Define the set $\mathcal{R}$ by $\mathcal{R} = \{(x,y) \in X \times X : x$ and $y$ have the same remainder when divided by $3\}$. Then the number of elements in $\mathcal{R}$ is $40$ $36$ $34$ $33$
asked Sep 23, 2019 in Set Theory & Algebra Arjun 248 views
1 vote
3 answers
12
Let $A$ be a set of $n$ elements. The number of ways, we can choose an ordered pair $(B,C)$, where $B,C$ are disjoint subsets of $A$, equals $n^2$ $n^3$ $2^n$ $3^n$
asked Sep 23, 2019 in Combinatory Arjun 272 views
0 votes
0 answers
13
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X$. Define $f: X \times \mathcal{P}(X) \to \mathbb{R}$ by $f(x,A)=\begin{cases} 1 & \text{ if } x \in A \\ 0 & \text{ if } x \notin A \end{cases}$ Then $f(x, A \cup B)$ equals $f(x,A)+f(x,B)$ $f(x,A)+f(x,B)\: – 1$ $f(x,A)+f(x,B)\: – f(x,A) \cdot f(x,B)$ $f(x,A)\:+ \mid f(x,A)\: – f(x,B) \mid $
asked Sep 23, 2019 in Set Theory & Algebra Arjun 177 views
0 votes
0 answers
14
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1 \} \:\:\:\:\:\:\:\: B = \{ (x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is non-empty none of the above
asked Sep 23, 2019 in Set Theory & Algebra Arjun 168 views
0 votes
2 answers
15
The set $\{(x,y): \mid x \mid + \mid y \mid \leq 1\}$ is represented by the shaded region in
asked Sep 18, 2019 in Set Theory & Algebra gatecse 82 views
0 votes
1 answer
16
Let $A$, $B$ and $C$ be three non empty sets. Consider the two relations given below: $\begin{array}{lll} A-(B-C)=(A-B) \cup C & & (1) \\ A – (B \cup C) = (A -B)-C & & (2) \end{array}$ Both $(1)$ and $(2)$ are correct $(1)$ is correct but $(2)$ is not $(2)$ is correct but $(1)$ is not Both $(1)$ and $(2)$ are incorrect
asked Sep 18, 2019 in Set Theory & Algebra gatecse 63 views
0 votes
0 answers
17
Suppose $f_{\alpha} : [0,1] \to [0,1],\:\: -1 < \alpha < \infty$ is given by $f_{\alpha} (x) = \frac{(\alpha +1)x}{\alpha x+1}$ Then $f_{\alpha}$ is A bijective (one-one and onto) function A surjective (onto ) function An injective (one-one) function We cannot conclude about the type
asked Sep 18, 2019 in Set Theory & Algebra gatecse 72 views
0 votes
1 answer
18
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of triangle $x,$ is one-one and into one-one and onto many-one and onto many-one and into
asked Sep 18, 2019 in Set Theory & Algebra gatecse 75 views
0 votes
1 answer
19
Let $A,B$ and $C$ be three non empty sets. Consider the two relations given below: $A-(B-C)=(A-B)\cup C$ $A-(B\cup C)=(A-B)-C$ Both (1) and (2) are correct. (1) is correct but (2) is not. (2) is correct but (1) is not. Both (1) and (2) are incorrect.
asked Sep 18, 2019 in Set Theory & Algebra gatecse 73 views
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