Use the deniability test to see whether the second sentence in each pair is an entailment of the first. [Assume that all the pronouns are intended to be anaphoric within the sentences.]
Nonnative speakers of English may prefer to run the tests on analogous sentences in their native language as a way of exploring the concepts where their intuitions are stronger.
Marcia thinks that she has lost her bike
Marcia has lost her bike.
I left the dining room after I ate my cookie
I ate my cookie.
Mark sliced the bread.
The bread was sliced.
Marcia regrets that she sold her bike.
Marcia sold her bike.
I left the dining room before I ate my cookie.
I ate my cookie.
Marcia hasn’t discovered that her bike has been stolen
Marcia’s bike has been stolen
Marcia has discovered that her bike has been stolen
Marcia’s bike has been stolen.
Margo stopped smoking.
Margo used to smoke.
Mark ate a few of the cookies
Mark ate some of the cookies.
Mark ate few of the cookies
Mark ate some of the cookies.
Mark ate several of the cookies.
Mark didn’t eat all of the cookies.
From deSwart, p. 69, do problems (5) and (6).
Show that the following pairs of formulas of the propositional logic are logically equivalent by providing truth tables:
NB: The ampersand (& ) has been substituted for the logical
conjunction symbol used in the text to insure that all browsers can
read the formulas correctly.