Chapter six was an interesting read for me. It let me hone in on specifics of a sentence which was a nice concept for me. One thing mentioned in chapter six was necessary and sufficient conditions. I thought this was interesting. I liked the example that they used in the book referring to taking an eye test and getting your drivers license.
A is necessary for B means If not A, then not B is true
A is sufficient for B means If a, then B is true.
A claim and its contrapositive is equivalent. It is sometimes easier to understand a conditional via its contrapositive. A claim is conditional if it can be rewritten as an “if . . .then . . .”claim that must have the same truth-value. This brings us to a contradictory of a conditional which establishes if A, then B has a contradictory A but not B. This contradictory is a but statement which proves B to not necessarily be a true statement.
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