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Syllabus: Sets, Relations, Functions, Partial orders, Lattices, Monoids, Groups.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} &\textbf{2024-2} &\textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&0& 1&0&1&0&0.83&1
\\\hline\textbf{2 Marks Count} &1&1&2& 0 &2&1&0&1.16&2
\\\hline\textbf{Total Marks} & 3&3&4&1&4&3&\bf{1}&\bf{3}&\bf{4}\\\hline
\end{array}}}$$

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Recent questions in Set Theory & Algebra

#441
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Kenneth Rosen Edition 7 Exercise 2.3 Question 23 (Page No. 153)
Determine whether each of these functions is a bijection from$R$ to $R.$f(x) = 2x+1$f(x) = x^2+1$f(x) = x^3$f(x) = (x^2+1)/(x^2+2)$
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#442
236
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1 answers
1 votes
Kenneth Rosen Edition 7 Exercise 2.3 Question 22 (Page No. 153)
Determine whether each of these functions is a bijection from$R$ to $R.$f(x) = -3x+4$f(x) = -3x^2+7$f(x) = (x+1)/(x+2)$f(x) = x^5+1$
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#443
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Kenneth Rosen Edition 7 Exercise 2.3 Question 21 (Page No. 153)
Give an explicit formula for a function from the set of integers to the set of positive integers that isone-to-one, but not onto.onto, but not one-to-one.one-to-one and onto.neither one-to-one nor onto.
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#444
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Kenneth Rosen Edition 7 Exercise 2.3 Question 20 (Page No. 153)
Give an example of a function from $N$ to $N$ that isone-to-one but not onto.onto but not one-to-one.both onto and one-to-one (but different from the identity function).neither one-to-one nor onto.
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#445
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Kenneth Rosen Edition 7 Exercise 2.3 Question 17 (Page No. 153)
Consider these functions from the set of teachers in a school. Under what conditions is the function one-to-one if it assigns to a teacher his or ... in a group of buses taking students on a field trip.salary.social security number
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#446
446
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Kenneth Rosen Edition 7 Exercise 2.3 Question 16 (Page No. 153)
Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns ... hermobile phone number.student identification number.final grade in the class.home town.
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#447
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Kenneth Rosen Edition 7 Exercise 2.3 Question 15 (Page No. 153)
Determine whether the function $f: Z \times Z \rightarrow Z$ is onto if$f(m,n) = m+n$f(m,n) = m^2+n^2.$f(m,n) = m.$f(m,n) = |n|.$f(m,n) = m-n.$
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#448
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Kenneth Rosen Edition 7 Exercise 2.3 Question 14 (Page No. 153)
Determine whether $f: Z \times Z \rightarrow Z$ is onto if$f(m,n) = 2m-n.$f(m,n) = m^2-n^2.$f(m,n) = m+n+1.$f(m,n) = |m|-|n|.$f(m,n) = m^2-4.$
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#449
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Kenneth Rosen Edition 7 Exercise 2.3 Question 13 (Page No. 153)
Determine whether each of these functions from $Z$ to $Z$ is onto??$f(n) = n-1$f(n) =n^2+1$f(n)= n^3$f(n) =\left \lceil n/2 \right \rceil$
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#450
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Kenneth Rosen Edition 7 Exercise 2.3 Question 12 (Page No. 153)
Determine whether each of these functions from $Z$ to $Z$ is one-to-one.$f(n) = n-1$f(n) =n^2+1$f(n)= n^3$f(n) =\left \lceil n/2 \right \rceil$
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#451
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1 answers
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Kenneth Rosen Edition 7 Exercise 2.3 Question 10 (Page No. 153)
Determine whether each of these functions form $[a,b,c,d]$ to itself is one-to-one.$f(a)=b, f(b)=a,f(c)=c,f(d)=d$f(a)=b, f(b)=b,f(c)=d,f(d)=c$f(a)=d, f(b)=b,f(c)=c,f(d)=d$
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#452
221
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Kenneth Rosen Edition 7 Exercise 2.3 Question 9 (Page No. 153)
Find the values.$\left \lceil 3/4 \right \rceil$\left \lfloor 7/8 \right \rfloor$\left \lceil -3/4 \right \rceil$ ... \right \rfloor$\left \lfloor 1/2.\left \lfloor 5/2 \right \rfloor \right \rfloor$
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#453
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Kenneth Rosen Edition 7 Exercise 2.3 Question 8 (Page No. 153)
Find the values.$\left \lfloor1.1 \right \rfloor$\left \lceil 1.1 \right \rceil$\left \lfloor -0.1 \right \rfloor$ ...
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#454
414
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0 answers
2 votes
Kenneth Rosen Edition 7 Exercise 2.3 Question 1 (Page No. 153)
Find the domain and range of these functions.the function that assigns to each pair of positive integers the maximum of these two integersthe function that assigns to ... and that assigns the value 0 to a bit string consisting of all 0s
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#455
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0 answers
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Kenneth Rosen Edition 7 Exercise 2.3 Question 6 (Page No. 152)
Find the domain and range of these functions.the function that assigns to each pair of positive integers the first integer of the pairthe function that assigns to ... that assigns to a bit string the longest string of ones in the string
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#456
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Kenneth Rosen Edition 7 Exercise 2.3 Question 5 (Page No. 152)
Find the domain and range of these functions. Note that in each case, to find the domain, determine the set of elements assigned values by the ... that assigns to each positive integer the largest perfect square not exceeding this integer
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#457
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Kenneth Rosen Edition 7 Exercise 2.3 Question 4 (Page No. 152)
Find the domain and range of these functions. Note that in each case, to find the domain, determine the set of elements assigned values by the function.the ... stringthe function that assigns to a bit string the number of bits in the string
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#458
255
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Kenneth Rosen Edition 7 Exercise 2.3 Question 3 (Page No. 152)
Determine whether $f$ is a function from the set of all bit strings to the set of integers if$f(S)$is the position of a $0$ bit in $S$.$f(S)$is the number of $1$ ... is $1$ and $f(S)=0$ when $S$ is the empty string, the string with no bits.
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#459
267
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Kenneth Rosen Edition 7 Exercise 2.3 Question 2 (Page No. 152)
Determine whether $f$ is a function from $Z$ to $R$ if$f(n) = +-n.$f(n) = \sqrt{n^2+1}.$f(n) = 1/(n^2-4).$
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#460
259
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Kenneth Rosen Edition 7 Exercise 2.3 Question 1 (Page No. 152)
Why is $f$ not a function from $R$ to $R$ if$f(x) =1 /x?$f(x) = \sqrt{x} ?$f(x) =± \sqrt{(x^2+1)}? $
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