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Order 5 of the following sentences so that they form a logical proof of the statement:

Suppose $R$ is a relation on $A = \mathbb{N}$ defined by $(x,y) \in R \Leftrightarrow y < x$ .

Prove that $R$ is transitive.

Choose from these statements.

$y < x$ and $z < y$
$x < y$ and $y < z$
$z < y < x \Rightarrow z < x$
Meditation leads to the next step.
Assume $\exists x,z \in \mathbb{N} \ni (x,z) \in A$
$R$ is transitive
Let $x,y,z \in \mathbb{N} \ni (x,y) \in R$ and $(y,z) \in R$
Let $x,y,z \in \mathbb{N} \ni (x,y) \in R, (y,z) \in R$ and $(x,z) \in R$
$(x,z) \in R$

The proof statements in correct order.

Choose from these statements.

$y < x$ and $z < y$
$x < y$ and $y < z$
$z < y < x \Rightarrow z < x$
Meditation leads to the next step.
Assume $\exists x,z \in \mathbb{N} \ni (x,z) \in A$
$R$ is transitive
Let $x,y,z \in \mathbb{N} \ni (x,y) \in R$ and $(y,z) \in R$
Let $x,y,z \in \mathbb{N} \ni (x,y) \in R, (y,z) \in R$ and $(x,z) \in R$
$(x,z) \in R$

The proof statements in correct order.