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Highest voted questions in Discrete Mathematics

27 votes
5 answers
262
GATE CSE 1995 | Question: 21
Let $G_1$ and $G_2$ be subgroups of a group $G$. Show that $G_1 \cap G_2$ is also a subgroup of $G$. Is $G_1 \cup G_2$ always a subgroup of $G$?.
Let $G_1$ and $G_2$ be subgroups of a group $G$.Show that $G_1 \cap G_2$ is also a subgroup of $G$.Is $G_1 \cup G_2$ always a subgroup of $G$?.
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27 votes
3 answers
264
GATE CSE 1993 | Question: 8.4
Let A be a finite set of size n. The number of elements in the power set of $A\times A$ is: $2^{2^n}$ $2^{n^2}$ $\left(2^n\right)^2$ $\left(2^2\right)^n$ None of the above
Let A be a finite set of size n. The number of elements in the power set of $A\times A$ is:$2^{2^n}$$2^{n^2}$$\left(2^n\right)^2$$\left(2^2\right)^n$None of the above
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27 votes
3 answers
266
GATE CSE 2007 | Question: 2
Let $S$ be a set of $n$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $S$ are: $n$ and $n$ $n^2$ and $n$ $n^2$ and $0$ $n$ and $1$
Let $S$ be a set of $n$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $S$ are:$n$ and $n$$n^2$ and $n$$n^2$ and $0$$n$ an...
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27 votes
4 answers
267
GATE CSE 2010 | Question: 4
Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ forms A Group A Ring An integral domain A field
Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ formsA GroupA R...
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27 votes
4 answers
268
GATE CSE 2009 | Question: 1
Which one of the following is NOT necessarily a property of a Group? Commutativity Associativity Existence of inverse for every element Existence of identity
Which one of the following is NOT necessarily a property of a Group?CommutativityAssociativity Existence of inverse for every element Existence of identity
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26 votes
2 answers
274
GATE CSE 1987 | Question: 9e
How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
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26 votes
5 answers
276
TIFR CSE 2012 | Part B | Question: 3
For a person $p$, let $w(p)$, $A(p, y)$, $L(p)$ and $J(p)$ denote that $p$ is a woman, $p$ admires $y$, $p$ is a lawyer and $p$ is a judge respectively. Which of the following is the correct translation in first order logic of ...
For a person $p$, let $w(p)$, $A(p, y)$, $L(p)$ and $J(p)$ denote that $p$ is a woman, $p$ admires $y$, $p$ is a lawyer and $p$ is a judge respectively. Which of the foll...
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26 votes
3 answers
279
GATE IT 2006 | Question: 24
What is the cardinality of the set of integers $X$ defined below? $X=\{n \mid 1 \leq n ≤ 123, n$ is not divisible by either $2$, $3$ or $5\}$ $28$ $33$ $37$ $44$
What is the cardinality of the set of integers $X$ defined below?$X=\{n \mid 1 \leq n ≤ 123, n$ is not divisible by either $2$, $3$ or $5\}$$28$$33$$37$$44$
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26 votes
8 answers
280
GATE CSE 1996 | Question: 1.1
Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to $A \cup B$ $A^c \cup B^c$ $A \cap B$ $A^c \cap B^c$
Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to$A \cup B$$A^c \cup ...
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