Mr. Nance,

My student has a question on Exercise 4 number 14. Her answer for was ~C ⊃ S instead of S ⊃ ~C. Can the statements “I will go swimming only if the water is not cold” be considered logically equivalent to “If the water is not cold, I will go swimming”?

Also, how can I explain the difference between “If the water is not cold I will go swimming” and “I will go swimming unless the water is cold”?

Thank you!

**Let me answer your second question first. You don’t need to explain the difference between “If the water is not cold then I will go swimming” and “I will go swimming unless the water is cold” because these are logically equivalent. The rule is this:**

*p unless q*is equivalent to*if not q then p*. You used this rule correctly. The statement “You will starve unless you eat sometime” means “If you do not eat sometime, then you will starve.”**But the statement “I will go swimming only if the water is not cold” is not logically equivalent to “If the water is not cold, then I will go swimming” because there might be other restrictions to swimming. The statement form p only if q is NOT equivalent to if q then p. The form p if q (without the “only”) IS equivalent to if q then p, but the “only” switches the order. The rule is this: p only if q is equivalent to if p then q. For example, the statement “He is a father only if he is a man” (which is true) is not equivalent to “If he is a man then he is a father” (which can be false). It is equivalent to “If he is a father then he is a man” (which is true).**

**In summary:**

*p unless q*=*if not q then p*

*p only if q = if p then q***Blessings!**