Intro to Logic Conditionals

[Sc] unless [Sa]

(¬[Sa]→[Sc]) — negate antecedent, swap position of before and after

Translate: Charlie eats lollipops, unless he eats a pastry

~Ecp → Ecl — negate antecedent, swap position of before and after

[Sa] otherwise [Sc]

(¬[Sa]→[Sc]) — negate antecedent, keep position of before and after

Translate: Charlie eats a pastry, otherwise he eats a lollipop

~Ecp → Ecl — negate antecedent, keep position of before and after

If [Sa] then [Sc]. Otherwise, [So]

([Sa]→[Sc])

(¬[Sa]→[So])

If Charlie eats a pastry, then he does not eat a lollipop. Otherwise, Charlie eats a bonbon.

(Ecp → ~Ecl) & (~Ecp → Ecb) — Two sentence otherwise

If Charlie eats a pastry, then he does eat a lollipop. Otherwise, Charlie eats a bonbon.

(Ecp → Ecl) & (~Ecp → Ecb) — Two sentence otherwise

[Sc] but not/except if [Sa]

([Sa]→¬[Sc])

(¬[Sa]→[Sc])

Charlie eats a lollipop, but not if he eats a pastry

(Ecp → ~Ecl) & (~Ecp → Ecl)

[Sa] but not [Sc]

¬([Sa]→[Sc])

Charlie eats a pastry, but not a lollipop

~ (Ecp → Ecl)

If (John taking the plea deal is necessary for him to not be imprisoned,) then (the plea deal is good for John.)

(~Ij → Tpj) → Gpj