Lounie G.

asked • 03/06/18

Set Builder Notations

1) Find 3 different elements that are in both 6Z and 8Z (where Z is an integer). Is there a convenient way to describe the set of all elements that are in both 6Z and 8Z?
 
2) For k is a natural number, define Tk={z is an integer | |z - sq.root of 2| < k}. Find a formula expressing |Tk| in terms of the value of k.

1 Expert Answer

By:

Andrew M.

6Z and 8Z, Z is an integer
 
With taking this to include all even numbers 2Z...
What if Z = 1?
6Z = 6   This is not in the set 8Z if Z is an integer
8Z = 8   This is not in the set 6Z if Z is an integer
This does not work
 
What we need are the multiples of the lowest common
multiple of 6 and 8... the multiples of 24
...,-72, -48, -24, 0, 24, 48, 72, ...
 
The intersection of 6Z and 8Z where Z is an integer is the set of 24Z where Z is an integer
6Z ∩ 8Z; Z∈ I = 24Z; Z∈ I
 
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03/07/18

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