Let n be a positive integer. Describe using quantifiers:1. x ∈ ⋃ k = 1...

Libby Owens

Libby Owens

Answered

2022-07-15

Let n be a positive integer. Describe using quantifiers:
1. x k = 1 n A k
2. x k = 1 n A k
My work: i = { 1 , 2 , 3 , , n }
1. ( x ) , ( x A i )
2. ( x ) , ( x A i )
What I need help is explaining with words. Currently I have:
a) There exists i for every x A i
b) There always is i for every x in A i

Answer & Explanation

minotaurafe

minotaurafe

Expert

2022-07-16Added 22 answers

Step 1
Your answer is not correct. It should be, given I := { 1 , 2 , , n },
1. k I , x A k
2. k I , x A k
Step 2
In words, that is
1. There exists a 1 k n such that x is in A k
2. For all 1 k n, x is in A k

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