All sorts of conditions may be necessary for others, but do not - by themselves - suffice for , or guarantee , those others. The foregoing is a complete set of necessary conditions, i. Frequently the terminology of "individually necessary" and "jointly sufficient" is used. One might say, for example, "each of the members of the foregoing set is individually necessary and, taken all together, they are jointly sufficient for x's being a square.
However, we must not generalize from this simple example and believe that it is usually, or often, a straightforward task to specify sets of conditions that are individually necessary and jointly sufficient.
Sometimes it is much easier to specify some, or many, of the necessary conditions even though we are unable to specify a set that is jointly sufficient. Other times, the converse is true: for some cases it will be easier to specify sufficient conditions without our being able to specify individually necessary ones.
Necessary conditions that are not sufficient Example 4. Here is the list of necessary conditions that White offered irrelevant conditions have been here removed, and the list has been renumbered : The Walkman is in good working order.
The batteries are good. The tape has music on it and is in good working condition. You operate the controls correctly. White, p. White then goes on to make a too-hasty claim: " Unfortunately, for his illustrative purposes, the list is by no means sufficient.
Here are just a few of the many additional necessary conditions that my own students, in previous years, have offered: The listener must not be deaf. The ambient surrounding sound must not drown out the earphones. The listener must be wearing the earphones, or must be close enough to them, to hear the music.
There must be nothing blocking the sound in the listener's ears. The tape must be inserted correctly; the door of the Walkman must be closed; and the tape must not be at the end of the reel more specifically, it must be positioned so that some of the parts of the tape which contain recorded music will pass over the playback heads. The earphones are in good working order.
The listener does not die in the time between operating the controls correctly and the music's emerging from the earphones. Even this expanded list is not complete.
I imagine that will little effort, you yourself can come up with still further necessary conditions. Who said food keeps us alive? Tom died a few days ago and he was not short of good food. I don't know why the car won't run; I just filled the gas tank.
Why don't you want to spend your life with me? I love you, and am I not good to you? The counselor told me that if I wanted to graduate I must have at least credit hours. Well, I've got that, but they're saying I won't walk this semester. How misleading! The job description said that they were looking for someone with a Master's degree. I've got my MA, but I cannot understand why they did not hire me. What does this sentence convey? The answer is pretty much similar to what we have discussed in the previous section.
Does one have to necessarily eat too many sweets to lead to weight gain? Not really! As discussed previously, there could be other reasons that could lead to weight gain. There can be alternate causes that can lead to weight gain As discussed, One may eat a lot of fat-laden products and consequently, gain weight. One might gain weight by not exercising enough. As discussed before, X is not the only way for Y to occur.
Again, think along the lines of the weight gain example. Michelle could carry an umbrella because of other reasons: She could carry an umbrella when the sun shines hard and therefore it is hot. She could be suffering from a migraine, which is triggered by the sun, and therefore could carry an umbrella. Thus, rain is a sufficient but not necessary condition for Michelle to carry an umbrella If you want to ace the GMAT, you should know long will you take to prepare for it. What can be inferred from this statement?
Ronaldo playing against Barcelona is definitely going to lead to a win for Real Madrid. What cannot be inferred from this statement is If Real Madrid won the match against Barcelona, then Ronaldo must have definitely played. Not at all! The match could have been won even without Ronaldo playing against Barcelona.
Maybe Barcelona did not play as well as expected that day and lost to Real Madrid. When there is a scarcity of water, the yields from the rice fields will be low. What cannot be inferred from the statement is If the yields from the rice fields were low, then there must have been shortage of water for that particular seed time. That is, If not X, then not Y If the outcome is achieved, then the sufficient condition must have been fulfilled.
Several of the politicians now recommending that the pundra be allowed to become weak made that same recommendation before each of the last two periods of currency weakness.
The goal is — Similar increase in exports The plan is — Make the pundra weak again. The conclusion therefore is: If pundra is made weak, exports will rise. It also says even with Z alternate cause , Y increase exports is possible. Or in other words, Y can happen without X And as we learned previously, a sufficient condition does not mean that other conditions are not present. But does it actually weaken the recommendation of the politicians? Which of the following can be most logically concluded from the statements above?
A brain that is mentally more active as it ages has higher potential to learn new things than the brain of same age that reduced its level of mental activity. Per the passage, as the brain ages, dendrites begin to reduce in size.
These dendrites are the antennas used by neurons to transmit information among themselves. This decrease in ability to learn new things is related to the decrease in size of dendrites. Increased mental activity has the propensity to reduce the dendrite shrinkage.
So, essentially, increased mental activity has the capacity to slow down the decrease in the ability to learn things Close but incorrect choice Option C Individuals whose mental activity levels do not increase as they grow older are likely to experience a decline in learning ability This option looks tempting because it also draws a seemingly similar but reverse relationship between the level of brain activity and the ability to learn new things by a brain.
But there is a change here. And so, we feel the reverse should also be true, i. Hence, this answer choice is incorrect. Takeaway — Sufficient but not Necessary Conditions When we are looking at passages in which the outcomes depend on certain conditions, then it is important for us to be able to evaluate whether those conditions are sufficient or necessary. The OG examples give us an overview of the kind of language used to present sufficient but not necessary conditions From this article, we have learned the following: How to identify whether the condition presented is a sufficient one but not a necessary one How to apply the understanding of the above to analyze the passage and the answer choices in the context of the passage.
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