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Recent questions in Discrete Mathematics

1 votes
3 answers
5321
Probability Expectaiton
A box contain 2 red balls and 3 white balls. The random experiment is picking two balls from the box. When 2 white balls picked, the balls will be replaced and experiment repeated. Otherwise stop the experiment. What is the expected number of repetations?
A box contain 2 red balls and 3 white balls. The random experiment is picking two balls from the box. When 2 white balls picked, the balls will be replaced and experiment...
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1 votes
2 answers
5322
#Deragement How many ways we put letter
How many ways we can put 5 letters L1 ,L2, L3, L4 ,L5 in 5 envelope e1, e2, e3, e4, e5 (at 1 letter per envelope) so that At most 1 letter is correctly placed At least 1 Letter is wrongly placed
How many ways we can put 5 letters L1 ,L2, L3, L4 ,L5 in 5 envelope e1, e2, e3, e4, e5 (at 1 letter per envelope) so thatAt most 1 letter is correctly placedAt least 1 L...
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1 votes
1 answer
5324
GATEBOOK
Given answer a C but iam getting A
Given answer a C but iam getting A
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2 votes
1 answer
5325
Quiz Question
Which of the following interference system is invalid? $R \rightarrow S, \sim \vdash \sim R$ $\sim R, P \rightarrow Q, Q \rightarrow R \vdash \sim P$ ... Iam getting answer as c but given b.
Which of the following interference system is invalid?​​$R \rightarrow S, \sim \vdash \sim R$$\sim R, P \rightarrow Q, Q \rightarrow R \vdash \sim P$$\sim R \rightar...
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2 votes
1 answer
5326
Group theory
Let the number of non-isomorphic groups of order 10 be X and number of non-isomorphic groups of order 24 be Y then the value of X and Y a) 3,2 b)2,7 c)1,7 d)4,5
Let the number of non-isomorphic groups of order 10 be X and number of non-isomorphic groups of order 24 be Y then the value of X and Ya) 3,2b)2,7c)1,7d)4,5
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2 votes
1 answer
5327
Group theory
Let $G$ be a group whose presentation is $G=\{ x, y \mid x^5 =y^2 =e, \:\:\:\: x^2y=yx\}$, $\mathcal{Z}_n$: Set of integers modulo $n$ Then $G$ is isomorphic to $\mathcal{Z}_5$ $\mathcal{Z}_{10}$ $\mathcal{Z}_2$ $\mathcal{Z}_{30}$
Let $G$ be a group whose presentation is$G=\{ x, y \mid x^5 =y^2 =e, \:\:\:\: x^2y=yx\}$,$\mathcal{Z}_n$: Set of integers modulo $n$Then $G$ is isomorphic to$\mathcal{Z}_...
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3 votes
2 answers
5328
Self
∀x∃y P(x) → Q(y) ≡ ∀x P(x) → ∃yQ(y) We have to prove whether this is a tautology or not. How do we proceed ?
∀x∃y P(x) → Q(y) ≡ ∀x P(x) → ∃yQ(y)We have to prove whether this is a tautology or not.How do we proceed ?
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1 votes
2 answers
5329
wff
A WFF that is equivalent to the WFF x=>y is: (A) y=>x (B) ~y=>x (C) ~y=>~x (D) y=>~x
A WFF that is equivalent to the WFF x=>y is:(A) y=>x (B) ~y=>x(C) ~y=>~x (D) y=>~x
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4 votes
2 answers
5330
generalised pigeonhole principle
Show that if seven integers are selected from the first 10 positive integers, there must be at least two pairs of these integers with the sum 11. Attempt-:partition will be {(1,10),(2,9),(3,8)(4,7)(5,6)} now how to apply pigeonhole principle to find the answer?
Show that if seven integers are selected from the first10 positive integers, there must be at least two pairsof these integers with the sum 11.Attempt-:partition will be ...
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1 votes
1 answer
5332
Counting
How many ways are there to seat six people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors? It would be better if one provide a pictorial explanation.
How many ways are there to seat six people around a circular table where two seatings are considered the samewhen everyone has the same two neighbors without regard to wh...
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2 votes
0 answers
5335
Counting Theory
10 Points were selected in the sequence with each side 1 unit, there will be atleast two points (of those points) such that distance between them can not exceeds.. 1/(2.sqrt(2)) (sqrt(2))/3 1/3 (sqrt(2))/9
10 Points were selected in the sequence with each side 1 unit, there will be atleast two points (of those points) such that distance between them can not exceeds..1/(2.sq...
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2 votes
1 answer
5336
Counting Theory
5 points were selected in an equilateral triangle with each side 1 units. There will at least 2 points (of those points) such that the distance between them can not exceed 1/2 1/3 1/4 None
5 points were selected in an equilateral triangle with each side 1 units. There will at least 2 points (of those points) such that the distance between them can not excee...
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3 votes
1 answer
5339
Combinatorics
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1 votes
1 answer
5340
Kenneth Rosen: Counting-Chapter 5
How many license plates consisting of three letters followed by three digits contain no letter or digit twice?
How many license plates consisting of three letters followed by three digits contain no letter or digit twice?
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