- #1
lep11
- 380
- 7
Homework Statement
Prove that {x∈ℤ : 2|x} ∩ {x∈ℤ : 9|x} ⊂ {x∈ℤ : 6|x}.
It means that the intersection of the two sets is subset of the set containing integers that are divisible by 6.
The Attempt at a Solution
Basically I need to show that if an integer is divisible by 2 and 9, then it's also divisible by 6.
Proof:
let. x=2*9*n=18*n=(6*3*n)∈{x∈ℤ : 6|x} (n∈ℤ)
Q.E.D.
However, I don't think it's that simple.
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