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#Combinatorics and Counting # Permutations and Combinations
If each of ‘a’ points on a straight line is joined to each of ‘b’ points on another straight line, excluding the points on the given two lines,then which of the following represents the number of points of intersection of these lines? Select all that apply. (ab(a-1)(b-1))/4 (ab(a-1)(b-1))/2 ab C(a,2) * C(b,2)
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in
Combinatory
Feb 17, 2023
317
views
combinatory
counting
1
vote
2
DRDO CSE 2022 Paper 1 | Question: 12
Given two propositions $P$ and $Q$. "if $P$ then $Q$" denoted by $P \rightarrow Q$ is called Implication. Such implication and its ____________ are logically equivalent.
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in
Mathematical Logic
Jan 27, 2023
259
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drdocse-2022-paper1
mathematical-logic
propositional-logic
2-marks
fill-in-the-blanks
0
votes
3
Kenneth Rosen Edition 7 Exercise 2.1 Question 9 (Page No. 125)
Determine whether each of these statements is true or false. $0$ $ \epsilon$ $\phi$ $\phi$ $\epsilon$ {$0$} {$0$} $ \subset$ {$ \phi$} $\phi$ $\subset$ {$0$} {$0$} $\epsilon$ {$0$} {$0$} $\subset$ {$0$} {$\phi$} $\subseteq$ {$\phi$}
answered
in
Mathematical Logic
Jan 22, 2023
475
views
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
0
votes
4
Kenneth Rosen Edition 7 Exercise 1.2 Question 34 (Page No. 24)
Five friends have access to a chat room. Is it possible to determine who is chatting if the following information is known? Either Kevin or Heather, or both, are chatting. Either Randy or Vijay, but not both, are chatting ... either both chatting or neither is. If Heather is chatting, then so are Abby and Kevin. Explain your reasoning.
answered
in
Mathematical Logic
Jan 20, 2023
8.5k
views
kenneth-rosen
discrete-mathematics
mathematical-logic
propositional-logic
0
votes
5
Mathematics for Natural Science
Suppose $x, y, z > 1$ are integers, let: $p(x,y)$ : $x$ is a factor of $y$ $q(x,y,z)$ : $z$ = $\text{GCD}(x,y)$ $r(x)$ : $x$ is prime. Check if the following argument is valid or not. $(\forall x \exists y)p(x,y) \implies r(x)$ ... $(\exists x)(\forall y)(p(x,y) \lor r(x))$ $\therefore (\forall y)(\exists z)(\exists x)q(x,y,z)$
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in
Mathematical Logic
Aug 23, 2022
358
views
mathematical-logic
discrete-mathematics
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