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Results tagged with discrete-mathematics
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user 928305
The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.
1
vote
Existential Quantifier Distributivity in First Order Logic
It looks a bit weird, because you introduce $x_1$ and $x_2$ separately from the statement $(x_1=x_2)$. Something better would be to write:
$$\exists x, P(x) \wedge Q(x)= \exists x_1, \exists x_2, P(x_ …
- 1,197
4
votes
Accepted
Maximize sum of paired products without replacement from $\{1,\ldots,2n\}$
Let’s take four positive numbers, say $a,b,c$ and $d$, such that $a \leq b \leq c \leq d$. Then:
$$(d-a)(b-c) \leq 0 \Leftrightarrow ac+bd \leq ab+cd$$
$$(d-b)(a-c) \leq 0 \Leftrightarrow ad+bc \leq a …
- 1,197
1
vote
Condition for inverse function.
One cool example could be taken from functions that takes other functions as an argument. This is not an example from functions of a real value, so it might not be really what you’re expecting - but I …
- 1,197
1
vote
Show the intersection of $A$ and $B$ and the relative complement of $B$ in $A$ are disjoint ...
My approach to this problem would be to proceed by contradiction.
Assume $A \cap B$ and $A \setminus B$ are not disjoint. There exists $x \in (A \cap B) \cap (A \setminus B)$. Therefore, $x \in B$ be …
- 1,197