1a. The Bakery was out of ingredients so they couldn’t make any chocolate cupcakes.

1b. The Bakery was out of chocolate cupcakes.

1a entails 1b because if they ran out of ingredients to make chocolate cupcakes then it has to be true that the Bakery was all out of chocolate cupcakes. But if the bakery was all out of the chocolate cupcakes it does not necessarily mean that they ran out of ingredients. The baker could be home sick or they may have just sold out. Maybe they burnt that batch!

2a. Jessica’s girlfriend is very tall

2b. Jessica has a girlfriend

The trigger is the possessive apostrophe -s denoting that this is a girlfriend of Jessica.

3a. Mary stopped smoking cigarettes

3b. Mary used to smoke cigarettes

The trigger is “stopped” because it presupposes that Mary used to smoke.