Problem: Form I
Consider the statements (1) (3) (4) , where , and are propositions. How many of these imply the truth of ?
Form II
Consider the statements (1) and are true and is false (2) is true and and are false (3) is true and and are false (4) and are true and is false. How many of these imply the truth of the statement " is implied by the statement that implies " ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The implication is true when (i) the consequent, , is true and the antecedent, , is either true or false, and (ii) the consequent is false and the antecedent is false.
The implication is true when (i) the consequent, , is true and the antecedent, , is either true or false, and (ii) the consequent is false and the antecedent is false.
In (1) is false and is true so that is true. In (2) is true and is true, so that is true. In (3) is false and is false so that is true. In (4) is true and is true, so that is true.