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Previous GATE
+38
votes
5
answers
1
GATE20002.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
asked
Sep 14, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

4.3k
views
gate2000
settheory&algebra
easy
sets
+25
votes
3
answers
2
GATE20002.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having 1 equivalence class $R$ is an equivalence relation having 2 equivalence classes $R$ is an equivalence relation having 3 equivalence classes
asked
Sep 14, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

3.2k
views
gate2000
settheory&algebra
relations
normal
+26
votes
4
answers
3
GATE20002.4
A polynomial $p(x)$ satisfies the following: $p(1) = p(3) = p(5) = 1$ $p(2) = p(4) = 1$ The minimum degree of such a polynomial is $1$ $2$ $3$ $4$
asked
Sep 14, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

2.3k
views
gate2000
settheory&algebra
normal
polynomials
+23
votes
3
answers
4
GATE199214a
If $G$ is a group of even order, then show that there exists an element $a≠e$, $e$, the identity in $G$, such that $a^2 = e$.
asked
Sep 13, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

1.2k
views
gate1992
settheory&algebra
grouptheory
normal
descriptive
proof
+12
votes
5
answers
5
GATE199115,a
Show that the product of the least common multiple and the greatest common divisor of two positive integers $a$ and $b$ is $a\times b$.
asked
Sep 13, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

607
views
gate1991
settheory&algebra
normal
numbertheory
proof
descriptive
+12
votes
3
answers
6
GATE199101,xiv
If the longest chain in a partial order is of length $n$, then the partial order can be written as a _____ of $n$ antichains.
asked
Sep 12, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

1.4k
views
gate1991
settheory&algebra
partialorder
normal
descriptive
+21
votes
5
answers
7
GATE20082
If $P, Q, R$ are subsets of the universal set U, then $(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$ is $Q^c \cup R^c$ $P \cup Q^c \cup R^c$ $P^c \cup Q^c \cup R^c$ U
asked
Sep 11, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

2k
views
gate2008
normal
settheory&algebra
sets
+4
votes
1
answer
8
number of symmetric funtions
A function $f:\left\{0, 1\right\}^{n}\rightarrow \left\{0, 1\right\}$ is called symmetric if for every $x_{1}, x_{2},....,x_{n} \in \left\{0, 1\right\}$ and every permutation $\sigma$ of $\left\{1, 2,...,n\right\}$ ... $2^{n+1}$ $2^{n}$ $2^{2n}/n!$ $2^{2n}$ $n!$
asked
Aug 27, 2014
in
Set Theory & Algebra
by
Marv Patel
Loyal
(
6.9k
points)

290
views
normal
settheory&algebra
+24
votes
2
answers
9
GATE20131
A binary operation $\oplus$ on a set of integers is defined as $x \oplus y = x^{2}+y^{2}$. Which one of the following statements is TRUE about $\oplus$? Commutative but not associative Both commutative and associative Associative but not commutative Neither commutative nor associative
asked
Aug 7, 2014
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

2.2k
views
gate2013
settheory&algebra
easy
binaryoperation
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