Concept Networks Math Example 4

Solution

1. 1
   Conditional ($p \Rightarrow q$) is the central concept: a statement claiming $q$ follows from $p$.
2. 2
   Contrapositive ($\neg q \Rightarrow \neg p$) is logically equivalent to the conditional — same truth value, different form. It is a reformulation of the conditional.
3. 3
   Proof by contradiction assumes $\neg q$ (or $\neg p$) and derives a contradiction, thus establishing $q$ (or $p$). It uses the conditional structure indirectly, by negating the conclusion and deriving a false statement.