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Recent questions and answers in Set Theory & Algebra
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SELF DOUBT
https://gateoverflow.in/2314/gate199317 NOT GETTING THE SOLUTION FROM HERE ......................... Now, these include the no. of persons who eat all 3 items thrice. So, excluding those, we get, no. of persons who eat at least two items (by adding the no. of persons eating EXACTLY 2 dishes and the number of persons eating all 3 dishes) as 31−Y−2∗5=21−Y31−Y−2∗5=21−Y.
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eyeamgj
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5
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+7
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3
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2
TIFR2011B23
Suppose $(S_{1}, S_{2},...,S_{m})$ is a finite collection of nonempty subsets of a universe U. Note that the sets in this collection need not to be distinct. Consider the following basic step to be performed on this sequence. While there exist sets $S_{i} ... of subsets of a finite universe $U$ and a choice of $S_{i}$ and $S_{j}$ in each step such that the process does not terminate.
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Set Theory & Algebra
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jaco
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31
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193
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tifr2011
settheory&algebra
sets
0
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1
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3
Set Theory
If A = {1,2,3...n}, then number of equivalence relations possible on A , which are also surjection on A is ________________? How to approach this type of problems?
answered
Nov 9
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Set Theory & Algebra
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Deepakk Poonia (Dee)
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32
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discretemathematics
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1
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4
Bijective function
Let R be set of all real numbers, and A = B = R*R A function A> B is defined by f(a,b) = (a+b,ab) How to prove it is a bijective function?
answered
Nov 9
in
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2019_Aspirant
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215
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discretemathematics
functions
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5
Set Theory
A relation R on a set of positive integers is defined by (a,b) belongs to R iff a and b are relatively prime. Which of the following is true about R? a. Symmetric and Reflexive b. Symmetric and irreflexive c.Symmetric and transitive d. Symmetric and not transitive The Ans is given as (d) but I think (b) is true. Any thoughts?
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Nov 8
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dan31
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183
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0
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6
Kenneth RosenPg155P18
Consider all below functions are from $R \rightarrow R$ Determine whether these functions are onetoone, and onto. (a)$f(x)=3x+4$ >Bijection (b)$f(x)=3x^2+7$>Not onetoone and not onto (c)$f(x)=\frac{x+1}{x+2}$>onetoone but not onto (d)$f(x)=x^5+1$>Bijection Are my answers correct.?
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Nov 7
in
Set Theory & Algebra
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Ayush Upadhyaya
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85
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kennethrosen
discretemathematics
+6
votes
3
answers
7
GATE19871xxii
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ has All complex roots At least one real root Four pairs of imaginary roots None of the above
answered
Nov 7
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Set Theory & Algebra
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Radha mohan
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985
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307
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gate1987
polynomials
0
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0
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8
Rosen
for 3 sets show (AB)C=(AC)(BC) using venn diagrams
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Nov 4
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9
Test series
R is a relation define on set A = {1,2,3}. The R is symmetric, transitive and irreflexive. Then R =
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Nov 4
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Set Theory & Algebra
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Shaik Masthan
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104
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relations
#counting
discretemathematics
+16
votes
2
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10
GATE20004
Let $S= \{0, 1, 2, 3, 4, 5, 6, 7\}$ and $⊗$ denote multiplication modulo $8,$ that is, $x ⊗ y= (xy) \mod 8$ Prove that $( \{ 0, 1\}, ⊗)$ is not a group. Write three distinct groups $(G, ⊗)$ where $G ⊂ S$ and $G$ has $2$ elements.
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Nov 4
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Dharmendra Lodhi
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gate2000
settheory&algebra
descriptive
groups
+11
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2
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11
GATE199214b
Consider the set of integers $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent? group ring field lattice
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Nov 4
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Dharmendra Lodhi
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gate1992
settheory&algebra
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normal
0
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3
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12
ISRO2017Q4
The function f:[0,3]>[1,29] defined by f(x)=2*X^3 15*X^2+36*X+1 is a) injective and surjective b) injective but not surjective c) injective but not surjective d) neither injective nor surjective
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Nov 1
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13
made EASY
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38
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14
made easY
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Oct 31
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48
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1
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15
made easy
shouldnt the answer be 1??
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Oct 31
in
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33
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16
mADe eAsY
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44
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17
made easy
S1 IS TRUE AND S2 IS FALSE, RIGHT??
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Oct 31
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29
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+9
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2
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18
TIFR2014B15
Consider the set $N^{*}$ of finite sequences of natural numbers with $x \leq_{p}y$ denoting that sequence $x$ is a prefix of sequence $y$. Then, which of the following is true? $N^{*}$ is uncountable. $\leq_{p}$ is a total order. Every nonempty subset of $N ... nonempty subset of $N^{*}$ has a greatest lower bound. Every nonempty finite subset of $N^{*}$ has a least upper bound.
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Oct 31
in
Set Theory & Algebra
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avadh
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353
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534
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tifr2014
settheory&algebra
partialorder
+3
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1
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19
relation
answered
Oct 30
in
Set Theory & Algebra
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ananda9931
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23
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28.3k
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relations
+1
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0
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20
SELF DOUBT
https://gateoverflow.in/39595/gate2016228 CONSIDER THE FIRST SOLUTION IT EXPLAINS FOR 2ND AT LAST AND CONCLUDED THAT ATLEAST ONE VERTEX SHOULD BE OF ODD DEGREE BUT WHAT IF ALL WILL BE OF ODD ?? WILL IT BE NOT THE CASE LIKE 1.??
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Oct 30
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0
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21
function
Given that the function f and g , fog is composition of function, also f and fog is onetoone functions , then what can be said about g ? A) g is onetoone function B)can't say anything about g
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Oct 30
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Soumya Tiwari
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20
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22
made easy
please explain!!
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Oct 29
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Gate Fever
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47
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0
votes
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23
made easy
according to me answer should be 920??
[closed]
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Oct 29
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0
votes
1
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24
GATEBOOK2019DM25
How many ways can the letters {a, b, c, d, e} be placed into 3 identical boxes such that no box is empty ?
answered
Oct 28
in
Combinatory
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Mk Utkarsh
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23.1k
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41
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gb2019dm2
discretemathematics
permutationsandcombinations
0
votes
1
answer
25
GATEBOOK2019DM23
How many numbers in {1, 2, · · · ,10000} have their digits sum to 7 ? (ex: 502).
answered
Oct 28
in
Combinatory
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Mk Utkarsh
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gb2019dm2
discretemathematics
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votes
0
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26
GATEBOOK2019DM21
How many paths are there from the lower left corner to the upper right corner, moving only up or to the right ? Path can not go through any of the dotted lines A. B. C. D.
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Oct 28
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GATEBOOK
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24
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gb2019dm2
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0
votes
0
answers
27
GATEBOOK2019DM22
In how many ways can 2 red and 4 blue rooks be placed on an 8by8 board so that no two rooks can attach on another ? A. B. C. D.
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Oct 28
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GATEBOOK
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gb2019dm2
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1
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28
GATEBOOK2019DM24
The number of permutations of {1, 2, 3, 4, 5} in which at least one odd integer is in its natural position is
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Oct 28
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GATEBOOK
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gb2019dm2
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0
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1
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29
GATEBOOK2019DM26
In how many ways can 10 women and 4 men line up in a straight line so that no two men are consecutive? A. B. C. D.
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Oct 28
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GATEBOOK
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gb2019dm2
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0
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30
GATEBOOK2019DM27
50 people are to be divided (partitioned) into 5 teams of 10 players each. In how many ways can this be done if each team has a different name A. B. C. D. None
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Oct 28
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GATEBOOK
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gb2019dm2
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31
GATEBOOK2019DM28
A bowl contains 5 red balls and 7 silver ones. A woman chooses balls at random without looking at them. How many must she choose, to be sure of having at least 3 of the same color? A. 7 B. 11 C. 10 D. 5
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Oct 28
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GATEBOOK
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gb2019dm2
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0
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32
GATEBOOK2019DM29
How many bit strings of length 6 have more zeroes than ones?
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Oct 28
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gb2019dm2
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33
GATEBOOK2019DM210
How many license plates with 3 decimal digits followed by 3 letters do not contain both the number 0 and the letter O? A. 17047279 B. 14074279 C. 17074279 D. 12436759
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Oct 28
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gb2019dm2
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34
GATEBOOK2019DM211
A decimal number is called “increasing” if each digit is greater than the previous one (e.g. 24589 is one). How many 5 digit increasing numbers are there?
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Oct 28
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GATEBOOK
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35
GATEBOOK2019DM212
How many different even integers ≥ 4000 and < 7000 have four different digits? A. 128 B. 728 C. 328 D. 528
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gb2019dm2
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36
GATEBOOK2019DM213
How many ways are there to seat 10 people, consisting of 5 couples, in a row of seats (10 seats wide) if all couples are to get adjacent seats?
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Oct 28
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gb2019dm2
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37
GATEBOOK2019DM214
An integer is called snakelike if its decimal representation satisfies if is odd and if is even. How many snakelike integers between 1000 and 9999 have four distinct digits?
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gb2019dm2
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38
GATEBOOK2019DM215
A landscaper is planting a row of 12 trees including 4 birch trees and 8 pine trees. How many ways can this be done without having two birch trees next to each other? A. B. C. D.
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39
GATEBOOK2019DM216
How many solutions does the equation a+b+c+d+e+f = 2006 have where a, b, c, d, e, and f are all positive integers? A. B. C. D.
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40
GATEBOOK2019DM217
How many bit strings of length 5 are there, such that every 1 is followed immediately by a zero?
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