Tommy ate his vegetables ∨ Tommy didn’t get any dessert

Tommy ate his vegetables ∨ ¬ Tommy got dessert

V ∨ ¬ D
either V or not D

¬ (Mike heard either the phone or the doorbell)

¬ (Mike heard the phone ∨ Mike heard the doorbell)

¬ (P ∨ D)
not either P or D

Mike wasn’t home ∨ Mike wasn’t answering the phone

¬ Mike was home ∨ ¬ Mike was answering the phone

¬ H ∨ ¬ P
either not H or not P

The package was sent ∧ either the package is still on its way or it’s been lost in the mail

The package was sent ∧ (the package is still on its way ∨ the package has been lost in the mail)

S ∧ (W ∨ L)
both S and either W or L

Neither the House nor the Senate had acted on the bill ∧ the White House expressed confidence that the bill would pass

¬ either the House or the Senate had acted on the bill ∧ the White House expressed confidence that the bill would pass

¬ (the House had acted on the bill ∨ the Senate had acted on the bill) ∧ the White House expressed confidence that the bill would pass

¬ (H ∨ S) ∧ W
both not either H or S and W

¬ Sam will pass through without either stopping by or calling

¬ (Sam will pass through ∧ ¬ Sam will either stop by or call)

¬ (Sam will pass through ∧ ¬ (Sam will stop by ∨ Sam will call))

¬ (P ∧ ¬ (S ∨ C))
not both P and not either S or C

Davis will take you or give you directions ∨ Edwards will take you or give you directions

(Davis will take you ∨ Davis will give you directions) ∨ (Edwards will take you ∨ Edwards will give you directions)

(D ∨ G) ∨ (E ∨ V)
either either D or G or either E or V

We’ll have a can without an opener ∨ we’ll have an opener without a can

(we’ll have a can ∧ we won’t have an opener) ∨ (we’ll have an opener ∧ we won’t have a can)

(we’ll have a can ∧ ¬ we’ll have an opener) ∨ (we’ll have an opener ∧ ¬ we’ll have a can)

(C ∧ ¬ O) ∨ (O ∧ ¬ C)
either both C and not O or both O and not C

¬ either Jan or Ken had matches or a lighter

¬ (Jan had matches or a lighter ∨ Ken had matches or a lighter)

¬ ((Jan had matches ∨ Jan had a lighter) ∨ (Ken had matches ∨ Ken had a lighter))

¬ ((M ∨ L) ∨ (K ∨ G))
not either either M or L or either K or G

Both Ann and Bill were in town ∧ neither Ann nor Bill knew the other was in town

(Ann was in town ∧ Bill was in town) ∧ ¬ either Ann or Bill knew the other was in town

(Ann was in town ∧ Bill was in town) ∧ ¬ (Ann knew Bill was in town ∨ Bill knew Ann was in town)

(A ∧ B) ∧ ¬ (K ∨ N)
both both A and B and not either K or N

Tom will handle both the scheduling and the publicity ∨ Dick will handle both the scheduling and the publicity ∨ Harry will handle both the scheduling and the publicity

(Tom will handle the scheduling ∧ Tom will handle the publicity) ∨ (Dick will handle the scheduling ∧ Dick will handle the publicity) ∨ (Harry will handle the scheduling ∧ Harry will handle the publicity)

(T ∧ P) ∨ (D ∧ B) ∨ (H ∧ L)
(both T and S) or (both D and C) or (both T and S)

The scheduling will be handled by either Tom, Dick, or Harry ∧ the publicity will be handled by either Tom, Dick, or Harry

(the scheduling will be handled by Tom ∨ the scheduling will be handled by Dick ∨ the scheduling will be handled by Harry) ∧ (the publicity will be handled by Tom ∨ the publicity will be handled by Dick ∨ the publicity will be handled by Harry)

(T ∨ D ∨ H) ∧ (P ∨ B ∨ L)
both (T or D or H) and (P or B or L)

It was the butler ∨ it was the nephew

It was either the butler or the nephew

¬ (the alarm worked ∨ the sprinkler worked)

¬ (either the alarm or the sprinkler worked)

Neither the alarm nor the sprinkler worked

¬ the part arrived ∨ ¬ the part was the problem

The part didn’t arrive ∨ the part wasn’t the problem

Either the part didn’t arrive or it wasn’t the problem

Ann has a large car ∨ ¬ (Bill will ride with us ∧ Carol will ride with us)

Ann has a large car ∨ ¬ Bill and Carol will ride with us

Ann has a large car ∨ Bill and Carol won’t both ride with us

Either Ann has a large car or Bill and Carol won’t both ride with us

(it rained over night ∨ there was a heavy dew) ∧ it is wet

It rained over night or there was a heavy dew ∧ it is wet

It rained over night or there was a heavy dew but, either way, it is wet

(AAA ∧ Co. will profit from the deal ∧ ZZZ Inc. will profit from the deal) ∨ (the deal will fall through ∧ ¬ (AAA ∧ Co. will profit from the deal ∨ ZZZ Inc. will profit from the deal))

AAA ∧ Co. and ZZZ Inc. will both profit from the deal ∨ (the deal will fall through ∧ ¬ (either AAA ∧ Co. or ZZZ Inc. will profit from the deal))

AAA ∧ Co. and ZZZ Inc. will both profit from the deal ∨ (the deal will fall through ∧ neither AAA ∧ Co. nor ZZZ Inc. will profit from the deal)

AAA ∧ Co. and ZZZ Inc. will both profit from the deal ∨ the deal will fall through and neither AAA ∧ Co. nor ZZZ Inc. will profit from it)

Either AAA ∧ Co. and ZZZ Inc. will both profit from the deal, or the deal will fall through and neither will profit from it