There is a contest with 40 Pokemons. There are 18 Pokemons who like to fight in the sky, and 23 who like to fight on ground. Several of them like to fight in water. The number of those who like to fight in the sky and on ground is 9. There are 7 Pokemons who like to fight in the sky and in water, and 12 who like to fight on ground and in water. There are 4 Pokemons who like to fight in the sky, on ground, and in water. How many Pokemons like to fight in water How do i express this problem with discrete math?

detineerlf 2022-07-18 Answered
There is a contest with 40 Pokemons. There are 18 Pokemons who like to fight in the sky, and 23 who like to fight on ground. Several of them like to fight in water. The number of those who like to fight in the sky and on ground is 9. There are 7 Pokemons who like to fight in the sky and in water, and 12 who like to fight on ground and in water. There are 4 Pokemons who like to fight in the sky, on ground, and in water. How many Pokemons like to fight in water. How do i express this problem with discrete math?
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Answers (2)

yatangije62
Answered 2022-07-19 Author has 16 answers
Step 1
N ( s k y g r o u n d w a t e r ) = N ( s k y ) + N ( g r o u n d ) + N ( w a t e r ) N ( s k y g r o u n d ) N ( s k y w a t e r ) N ( g r o u n d w a t e r ) + N ( s k y g r o u n d w a t e r )
Step 2
where N(X) is number of pokemon that wants to fight in terrain X. This is called inclusion-exclusion principle.
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enmobladatn
Answered 2022-07-20 Author has 6 answers
Step 1
Assuming there every Pokemon wants to fight.
We can use principle of inclusion and exclusion to solve this problem. If x is the number of Pokemons like to fight in water then,
40 = 18 + 23 + x ( 9 + 7 + 12 ) + 4 x = 23
Step 2
If there are Pokemon who don't want to fight then we need to subtract that number from the RHS of the equation and then solve for x.
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