Conditional Statement Converse Inverse Contrapositive Hypothesis ...

. Complete the following sentence to make a true statement. Explain your reasoning. Is your answer
choice consistent with all of the examples of converse from your homework (1-5)?
Multiple choice: The converse of a false conditional statement is ____.
A) always also false
B) always true
C) sometimes true and sometimes false because whether the converse is true or false does not depend on
whether the original statement is true or false.
Whenever we talk about statements in general, without having a particular example in mind, it is useful to talk
about the propositional form of the statement.
For the propositional form “if p, then q”, the converse propositional form is “if q, then p.”
If two propositional forms result in statements with the same truth value for all possible cases of substituting
statements for the propositional variables, we say that the forms are logically equivalent.
If there exist statements that can be substituted into the propositional forms so that the resulting statements have
different truth values, we say that the propositional forms are not logically equivalent
c. Consider your answers to parts a and b, and decide how to complete the following statement to make
it true. Justify your choice.
The converse propositional form “if q, then p” is/is not (choose one) logically equivalent to the
conditional statement “if p, then q.”
d. Multiple choice: If you learn a new mathematical fact in the form “if p, then q”, what can you
immediately conclude, without any additional information, about the truth value of the converse?
A) no conclusion because the converse is not logically equivalent
B) conclude that the converse is true
C) conclude that the converse is false
e. In the opening of the passage from Alice in Wonderland, when Alice hastily replied
"I do, at least -- at least I mean what I say -- that's the same thing, you know."
What statements did Alice think were logically equivalent?
What was the Hatter saying about the equivalence of these statements when he replied to Alice by
saying "Not the same thing a bit!"?
There are two other important propositional forms related to any given conditional statement. We introduce
these by exploring other inhabitants of the land of functions.