In logic, necessity defines a relationship between two logical statements one of which can only be true if the other is true as well. When we say “*p* is necessary for *q,”* we mean that statement *q* cannot be true unless statement *p* is as well. If *p* is false then so is *q*. We can write this as an implication: ¬p→¬q.

Written as ¬p→¬q captures the dependence (necessity) of *q*‘s truth value on *p*, but taking the contrapositve yields a simpler conditional statement: *q*→*p*, *q* implies *p*.

For example, take the statement, “If something is a canoe it needs to be a boat.” This means that if something is not a boat then it is not a canoe, ¬*b*→¬*c*. The contrapositive statement is, “If something is a canoe then it is a boat,” *c*→*b*.

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