1.3

If Quentin quits his job provided that both Pam and Rebecca quit their jobs, then he quits his job.

(((D&F)->E)->E)

If John dances and so does Mary, but Bill does not, then Mary will not be happy but John and Bill will.

(((P&Q)&~R)->(~T&(S&U)))

If John dances on the condition that if he dances Mary dances, then he dances.

(((P->Q)->P)->P)

Mary will dance if John or Bill but not both dance.

(((PvR)&~(P&R))->Q)

If Mary dances only if Bill dances and John dances only if Mary dances, then John dances only if Bill dances.

(((Q->R)&(P->Q))->(P->R))

If both Pam and Rebecca win the lottery, then they both quit their jobs.

((A&C)->(D&F))

Either Pam or Quentin wins the lottery, but not both of them do.

((AvB)&~(A&B))

Rebecca quits her job, provided that she wins the lottery and Quentin quits his job.

((C&E)->F)

Though Rebecca wins the lottery but does not quit her job, Quentin does not win the lottery but does quit his job.

((C&~F)&(~B&E))

If Pam's winning the lottery is necessary for her quitting her job, then she does not quit her job.

((D->A)->~D)

Quentin quits his job only if Rebecca does too, but Rebecca quits her job only if she wins the lottery.

((E->F)&(F->C))

Mary will be happy if both John and Bill dance.

((P&R)->T)

If one of the three dances, at least one other will.

((P->(QvR))&((Q->(PvR))&(R->(PvQ))))

At least one of the three will dance.

((PvQ)vR)

If Mary dances although John is not happy, Bill will dance.

((Q&~S)->R)

If John's dancing is necessary for Mary to be happy, Bill will be unhappy.

((T->P)->~U)

Although neither Pam nor Rebecca wins the lottery, they both quit their jobs.

((~A&~C)&(D&F))

Neither Pam nor Rebecca either wins the lottery or quits her job.

((~A&~D)&(~C&F))

Neither Quentin nor Rebecca wins the lottery, but Pam does.

((~B&~C)&A)

Pam wins the lottery; also, she quits her job and so does Rebecca.

(A&(D&F))

If Pam, who is quitting her job, wins the lottery, then Rebecca will quit her job, too.

(D&(A->F))

Only if Pam wins the lottery will she quit her job.

(D->A)

If Quentin quits his job, then Rebecca quits her job but Pam does not.

(E->(F&~D))

Given that Quentin quits his job, neither Rebecca nor Pam quits her job.

(E->~(FvD))

Quentin quits his job provided that he wins the lottery, unless Rebecca does not quit her job.

(F->(B->E))

Rebecca quits her job only if either Pam or Quentin does not.

(F->(~DV~E))

John is dancing but Mary is not dancing.

(P&~Q)

John's dancing is sufficient to make Mary happy.

(P->T)

If Bill dances, then if Mary dances John will too.

(R->(Q->P))

John's dancing is necessary to make Mary happy.

(T->P)

Mary will be happy only if Bill is happy.

(T->U)

Mary will be happy if and only if John is happy.

(T<->S)

Neither Pam nor Rebecca quits her job unless Quentin wins the lottery and quits his job.

(~(B&E)->(~D&~F))

Unless Quentin wins the lottery and quits his job, Pam will not quit her job.

(~(B&E)->~D)

Although neither John nor Bill is dancing, Mary is happy.

(~(PvR)&T)

If neither John nor Bill is dancing, Mary is not happy.

(~(PvR)->~T)

Unless Quentin quits his job, both Pam and Rebecca quit their jobs.

(~E->(D&F))

If John does not dance, then Mary will not be happy.

(~P->~T)

John will not dance unless Mary is happy.

(~PvT)

Neither John nor Bill will dance if Mary is not happy.

(~T->~(PvR))

Mary is not happy unless either John or Bill is dancing.

(~Tv(PvR))

Provided that Bill is unhappy, John will not dance unless Mary is dancing.

(~U->(~PvQ))

It's not the case that either Pam or Rebecca quits her job.

~(DvF)