Question

Write this statement in your own words: ∃x ∈ ℕ, y ∈ ℤ|x² = y² Rewrite this using the appropriate mathematical notation: Even numbers are in the set of integers.

Answer 1

See below.

Explanation:

1)

So we have:

`\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2`

This can be interpreted as:

"There exists a natural number x and an integer y such that x² is equal to y²."

2)

So we want even numbers are in the set of integers.

`\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}`

This is interpreted as:

"The set of even numbers (2n such that n is an integer) is in the set of integers"