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ashhuizing
08.09.2019 •
Mathematics
Let x be a set of size 20 and a cx be of size 10. (a) how many sets b are there that satisfy a ç b ç x? (b) how many sets b are there such that a and b are not disjoint? show your reasoning in both cases. you may leave your answer as an expression (eg. 510 + 3(
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Ответ:
(a) Number of sets B given that
A⊆B⊆C: 2¹⁰. (That is: A is a subset of B, B is a subset of C. B might be equal to C)A⊂B⊂C: 2¹⁰ - 2. (That is: A is a proper subset of B, B is a proper subset of C. B≠C)(b) Number of sets B given that set A and set B are disjoint, and that set B is a subset of set X: 2²⁰ - 2¹⁰.
Step-by-step explanation:
(a)Let
denote the 20 elements of set X.
Let
denote elements of set X that are also part of set A.
For set A to be a subset of set B, each element in set A must also be present in set B. In other words, set B should also contain
.
For set B to be a subset of set C, all elements of set B also need to be in set C. In other words, all the elements of set B should come from
.
For each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus
possibilities for set B.
In case the question connected set A and B, and set B and C using the symbol ⊂ (proper subset of) instead of ⊆, A ≠ B and B ≠ C. Two possibilities will need to be eliminated: B contains all ten "maybe" elements or B contains none of the ten "maybe" elements. That leaves
possibilities.
(b)Set A and set B are disjoint if none of the elements in set A are also in set B, and none of the elements in set B are in set A.
Start by considering the case when set A and set B are indeed disjoint.
Set B might be an empty set. Once again, for each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus
possibilities for a set B that is disjoint with set A.
There are 20 elements in X so that's
possibilities for B ⊆ X if there's no restriction on B. However, since B cannot be disjoint with set A, there's only
possibilities left.
Ответ:
m(x-x1)=y-y1
where:
slope,m=(y-y1)/(x-x1)
m=(5.15-3.8)/(1997-1990)
m=0.193
taking 1978 as our x=0, 1990 will be x=12
thus the equation will be:
0.193(x-12)=y-3.8
0.193x-2.316=y-3.8
thus
y=0.193x+1.484
b]
The minimum wage in 2025 will be as follows:
x=2025-1978=47
thus plugging the values in the equation we get:
y=0.193(47)+1.484
y=10.555