Discrete Mathematics

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121

END

Step 5:

STOP

Example

10

LetA=

{1, 2, 3, 4,

5}

and B = {3, 5, 6, 7, 8, 9}. Verify Addition Principle (Inclusion-Exclusion

Principle).

I solution I

LetA

u B = {1, 2, 3, 4, 5, 6, 7, 8, 9} and

An

B = {3, 5}

Also,

I A

I=

5, I B

I=

6,

IAn

B

I=

9,

IAn

B

I=

2

Then

I A u B I = 9 = I A I + I B I + I A n B I = 5 +

6-

2

Note

If

A and B are disjoint sets, A n B = f

IAnBI=O

So Addition Principle becomes

IAuBI=IAI+IBI

Example

11

A software firm hires

30

programmers to handle systems programming tasks and

50

program-

mers for application programming.

Of

those hired, 15 will be expected ...