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1. It is not hot.

$\lnot$ p

2. It’s hot and it’s wet.

p$\land$ q

3. It is not wet and I am not tired.

$\lnot$ q$\land\lnot$ r

4. It’s not both hot and wet.

$\lnot$ (p$\land$ q)

5. I am tried and it is hot and it’s wet.

r$\land$ p$\land$ q

6 I am not tired but it is wet.

$\lnot$ r$\land$ q

7. It’s neither hot nor wet, but I am tired.

$\lnot$ p$\land\lnot$ q)$\land$ r

8. It’s not the case I am not tired.

$\lnot$ r

9. Either I am tired or it’s hot.

r$\lor$p

10. I am tired or it’s hot.

r$\lor$p

11. It is wet or it’s not hot.

q$\lor\lnot$ p

12. It’s either not wet or not hot.

$\lnot$ q$\lor\lnot$ p

13. It’s not the case that it’s either hot or wet.

$\lnot$( p$\lor$q)

14. It’s hot or wet but not both.

( p $\lor$ q)$\lnot$ (p$\land$ q)

15. It’s hot or wet or I am not tired.

p$\lor$q$\lor\lnot$ r

16. I am tired but it’s not hot or wet.

r$\land\lnot$ p$\lor$ q

17. It’s hot and wet or it’s hot and not wet.

( p$\land$ q)$\lor$ ( p$\land\lnot$ q)

18. Either it’s not wet or it’s both hot and wet.

$\lnot$ q$\lor$ (p$\land$ q)

19. It’s not the case that, I am tired but it’s not hot.

$\lnot$ r $\land\lnot$ p

20. Either it’s not both hot and wet, or it is.

$\lnot$ (p$\land$ q)$\lor$ (p$\land$q)