SOLUTION: List all elements of the set A ∩ B, where
A = {n ∈ N | ∃k ∈ N such that n = 2^k + 2},
B = {n ∈ N | ∃k ∈ N such that n = 2^k − 2}.
Algebra.Com
Question 1023501: List all elements of the set A ∩ B, where
A = {n ∈ N | ∃k ∈ N such that n = 2^k + 2},
B = {n ∈ N | ∃k ∈ N such that n = 2^k − 2}.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The first few elements of A are
, , , , , ,...
The first few elements of B are
, , , , ,...
It is quite clear that 6 is a common element, so 6 is in A ∩ B.
Now we show that for k and , there are no other common terms.
Suppose there are, or suppose there are natural numbers a, such that
==> ,
==> , contradiction, because and would both be even since a, .
Therefore A ∩ B = {6}.
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