Converse, Contrapositive and Negation

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If every printer is busy then there is a job in the queue.

where $B(p)$ = Printer $p$ is busy and $Q(j)$ = Print job $j$ is queued.

When it's translated to symbol, we'll have $(∀p B(p)) → (∃j Q(j))$.

I'm trying to translate this statement to both English and symbol forms for Converse, Contrapositive and Negation

Following is what i have got so far:
Converse
in words: If there is a job in the queue, then every printer is busy.
in symbol: $(∃j Q(j)) → (∀p B(p))$

Contrapositive
in words: If there is no job in the queue, then not every printer is busy.
in symbol: $¬(∃j Q(j)) → ¬(∀p B(p))$

Negation
in words: Every printer is busy and there is no job in the queue.
in symbol: (not sure)

It's the symbol part that i'm not sure if they are correct or not. Any advice would be appreciated!

$\endgroup$ 9 Sorted by: Reset to default

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