Any help on this would be greatly appreciated (^_^) Question 7: True/False 5pt _

ID: 3195359 • Letter: A

Question

Any help on this would be greatly appreciated (^_^)

Question 7: True/False

5pt ___ The principle of inclusion and exclusion applies to the union of any number of sets so long as all of them are finite.

5pt ___ The pigeonhole principle guarantees that if there are 8 people in a room, at least 3 of them were born on the same day of the week.

5pt ___ If there are more than 20 items placed in 20 slots, then at least 1 slot contains more than 1 item.

5pt ___ There must be 13 people in a room to guarantee that at least 2 of them were born in the same month.

a) TRUE

It is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets.

b)FALSE

The Pigeonhole Principle: If n + 1 objects are placed into n boxes, then some box contains at least 2 objects.

1 week = 7 days i.e n = 7 (box)

we have n+1 = 8 people(object)

Therefore two people were born on the same day of the week.

c) TRUE

slots , n= 20

items are more than 20 menas n+1 =21. then at least 1 slot contains more than 1 item.

d) True

There are n = 12 months ('boxes'), but we have n+1 = 13 people ('objects'). Therefore two people were born in the same month.

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