What is the least number n with the property that, in every group of n people, there are at least three people who are all frien
1 answer:
Answer:
hello your question is incomplete attached below is a the complete question
answer : n = 5
Step-by-step explanation:
lets consider N to be 5
To prove that the least number 'n' = 5
we will represent this information in a graph as vertex
Black edge = Friends
Blue edge = not Friends
From the attached diagram any vertex contains 0,1,2,3,4 black lines and 4,3,2,1,0 blue lines
attached below is an explanation related to the choice of n = 5
considering n = 5 is satisfied by the explanation given
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Answer:
(a) Set of rational numbers
(b)
Step-by-step explanation:
Solving (a): Set that is closed under subtraction
The solution to this is rational numbers.
For a set of number to be closed under subtraction, the following condition must be true
Where
a, b, c are of the same set.
The above is only true for rational numbers.
e.g.
The operations and the result in the above samples are rational numbers.
Solving (b): Choice not close under addition[See attachment for options]
As stated in (a)
For a set of number to be closed under subtraction, the following condition must be true
Where
a, b, c are of the same set.
In the given options (a) to (d), only
is not close under addition because:
is irrational while
is rational
<em>In other words, they belong to different set</em>
