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Necessary and Sufficient Condition Statements

Today, I want to discuss a very important concept of CR – analyzing a conditional statement. You will often encounter these even though they may not be in the exact same format as the one we will discuss below. We will discuss the basic framework and then we will look at questions where this concept will be very helpful. Mind you, without this framework, it can get a little tricky to wrap your head around these questions.



Statement 1: If you trouble your teacher, you will be punished.

What does this imply? It implies that ‘troubling your teacher’ is a sufficient condition to get punished. If you trouble, you will get punished.

What about the other way around? What if you got punished? Can we say that you troubled your teacher? No! You could have got punished for something else. Mind you, troubling your teacher is not a necessary condition to get punished. There could be other things that could lead to punishment.

On the same lines, what if you didn’t trouble your teacher? Can we say that you didn’t get punished? Hope it makes sense to you that it is not necessary that you didn’t get punished. You could have got punished for something else.

What if you didn’t get punished? Does that imply something? Sure! We can say that you didn’t trouble your teacher and you didn’t do anything else that could get you punished.


To write it succinctly,

Statement: If A, then B (A is sufficient for B to happen)

  • A implies B
  • B does NOT imply A
  • Not A does NOT imply Not B
  • Not B implies Not A

Notice that you can replace ‘if’ by ‘when’ or ‘whenever’.



Statement 2: Only if you work hard will you succeed.

What does this imply? It implies that hard work is a necessary condition to succeed. Note here that it may not be sufficient to succeed but it is definitely necessary. Along with hard work, you might need smarts and luck on your side too.

What if you know that Tom worked hard? Can you say he succeeded? No, it is not necessary. As discussed, only hard work may not have been enough. It was essential but it may still not have led to success.

What if you know that Tom succeeded? Can we say that he worked hard? Yes! Since he succeeded and hard work was essential to succeed, he must have worked hard.

Let’s look at it the other way now. What happens when Tom doesn’t work hard? We know that in that case he certainly doesn’t succeed. Hard work is essential to success. No hard work implies no success.

On the same lines, what about the case in which we know that Tom didn’t succeed? Can we say whether he had worked hard or not? No. He may or may not have worked hard. Since there could have been other conditions required to succeed, we don’t know what led to failure.


To write it succinctly,

Statement: Only if A, then B (A is necessary for B to happen)

  • A does NOT imply B
  • B implies A
  • Not A implies Not B
  • Not B does NOT imply Not A

Notice that you can replace ‘only if’ by ‘only when’.


I will leave you with a tricky CR question I came across in a forum. See whether you can figure it out.


Question: A newborn kangaroo, or joey, is born after a short gestation period of only 39 days. At this stage, the joey’s hind limbs are not well developed, but its forelimbs are well developed, so that it can climb from the cloaca into its mother’s pouch for further development. The recent discovery that ancient marsupial lions were also born with only their forelimbs developed supports the hypothesis that newborn marsupial lions must also have needed to climb into their mothers’ pouches.

The argument in this passage relies on which of the following assumptions?

(A) All animals that are born after a short gestation period are born with some parts of their bodies underdeveloped.
(B) Well developed forelimbs would have been more advantageous to ancient marsupial lions than well developed hind limbs would have been.
(C) If the newborn marsupial lion did not climb into its mother’s pouch, then paleontologists would be able to find evidence of this fact.
(D) Newborn marsupial lions that crawled into their mothers’ pouches could not have done so had they not had only their forelimbs developed at birth.
(E) Newborn marsupial lions would not have had only their forelimbs developed if this development were of no use to the marsupial lions.


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