This is a discrete math problem: 6.2 (5.2) Let 4-la,b,cj 1,23,4,5). Note typical

Question

This is a discrete math problem:

6.2 (5.2) Let 4-la,b,cj 1,23,4,5). Note typical members of A include (a.2).(a.5) and (c.3). a) What is the minimum number o same first coordinate? (3 points) f elements of A that must be selected to guarantee that at least two have the the Jome Second coor dinate must be selected to uarontes three with Girst coordinote would be accept able b) What is the minimum number of elements of A that must be selected to guarantee that at least three have same second coordinate? (3 points)

Explanation / Answer

Now for each a we can select 5 from the other set and similarly for other two elements

So 5 elements in A with a as first coordinate and similarly for other two ie b,c

a)

So in worst can we might select 1 with a as first and then 1 with b as first and 1 with c as first and have selected 3 elements but none with same first coordinate

But selecting one more will ensure two with same first coordinate

So a minimum 4 need to be selected

b)

Now for each element in second set there are three choices

We can select , in worst case, 2 of each with 1,2,3,4,5 as second coordinate respectively giving us 10 elements but with no 3 with same second coordinate.

But selecting one more will ensure atleast 3 with same second coordinate

So a minimum of 11 elements need to be selected

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