Set notation question: If A = {x∈ℕ: x is even } and B = {x∈ℕ: x is odd }...
If A = {x∈N: x is even } and B = {x∈N: x is odd }
Is it valid to write this as:
A = {x∈N:∃n∈N(x=2n)}
B = {x∈N:x∈N∧∃m∈N(x=2m+1)}
A∪B = {x∈N:(∃n∈N(x=2n))∨(x∈N∧∃m∈N(x=2m+1))}=N
A∩B= {x∈N:(∃n∈N(x=2n))∧(x∈N∧∃m∈N(x=2m+1))} = ∅
If A = {x∈N: x is even } and B = {x∈N: x is odd }
Is it valid to write this as:
A = {x∈N:∃n∈N(x=2n)}
B = {x∈N:x∈N∧∃m∈N(x=2m+1)}
A∪B = {x∈N:(∃n∈N(x=2n))∨(x∈N∧∃m∈N(x=2m+1))}=N
A∩B= {x∈N:(∃n∈N(x=2n))∧(x∈N∧∃m∈N(x=2m+1))} = ∅
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