The necessary and sufficient conditions are discussed in Hurley’s Intro to Logic.
"A is said to be a sufficient condition for B whenever the occurrence of A is all that is needed for the occurrence of B. B is said to be a necessary condition for A whenever A cannot occur without the occurrence of B" (23).
1 translation: Which of the following is a sufficient condition for getting a speeding ticket?(A)Driving a vehicle,(B) driving on a road,(C) driving 30 over the speed limit in the presence of a cop
Ask yourself, if this condition holds, then does the event have to happen? Must the event happen if the condition holds?
So when asking if it’s a sufficient condition, ask yourself the key question, "If this condition holds, must the event occur?"
The following are some examples from Hurley's chapter 1:
2 translation: Having a racket is a _____________ condition for playing tennis
If you have a racket, must the event occur? Of course not, as you could merely be holding onto a racket for someone else. Or, you could be a collector of tennis rackets.
When asking if it’s a necessary condition, remind yourself the key phrase, "The event cannot occur if the condition doesn’t hold."
3 translation: The condition doesn’t hold, and because of this the event cannot occur
4 translation: If the condition holds, then the event must occur
5 translation: Drinking water is a ___________ condition for quenching one’s thirst
6 translation: Pulling the cork is a ___________ condition for drinking an expensive bottle of wine
7 translation: Stepping on a cat’s tail is a ___________ condition for making the cat yowl
8 translation: Paying attention is a ___________ condition for understanding a lecture
Ask yourself, "if this condition holds(paying attention), then does the event have to happen? Must it happen? Of course not, the student paying attention might simply not be bright enough to understand the lecture.
If the condition doesn’t hold(not paying attention), then the event cannot occur.
9 translation: Taking a swim in the North Sea is a ____________ condition for cooling off
10 translation: Opening the door is a _________ condition for crossing the threshold
Ask yourself, "if this condition holds(opening the door), then does the event have to happen? No, one can open the door, and just stand there or run away.
If the condition doesn’t occur(not opening the door), then the even cannot occur(crossing the threshold). I found this problem a little confusing because I can imagine someone bursting through(not opening the door) the door and crossing the threshold.
I suppose common sense is needed for some of these practice problems.