16. Use induction to prove that if A 1 , A 2 , A 3 , ... , A n are sets, then: A

Question

16. Use induction to prove that if A1, A2, A3, ... , An are sets, then:

A1cA2c... Anc = [A1A2A3... An]c

      In other words:

n

n

[A   k]c

=

[   

Ak   

]c   

k= 1

k= 1

Note: the symbol c is the complement of a set (just like a negation)

Basis:

Assume:

Prove:

Proof:

  

n

     

     

     

     

n

     

     

     

     

[A   k]c

     

=

     

[   

     

     

Ak   

     

]c   

     

k= 1

     

     

     

     

k= 1

     

     

   Use induction to prove that if A1, A2, A3, ... , An are sets, then:

Explanation / Answer

HOPE YOU MEAN UNION BY SIGMA NOTATION .. ASSUMING SO .. USING ' TO INDICATE COMPLEMENT AND + TO DENOTE UNION TO SHOW THAT

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