About Anvaya/Vyatireka and Necessary/Sufficient Conditions
Amarnath S
BVK Sastry (G-S-Pop)
Namaste
On < Sanskrit Logic, versus Modern Mathematics …. Anvaya / Vyatireka logic related to Necessary and Sufficient Conditions in Mathematics? >
1. Related. Yes. Partially overlapping.
2. Related to < Necessary and sufficient conditions> - No. Technicalities are different.
Context matters. Numeracy, Maths and Statistics - Academic Skills Kit (ncl.ac.uk)
3. Example:
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See: If X, then Y | Sufficiency and necessity (article) | Khan Academy
We use the concept of necessary and sufficient conditions to help us describe relationships between statements.
Necessary Condition
Suppose that AA and BB are statements. We say that the statement AA is necessary for the statement BB if BB cannot be true unless AA is also true. In other words, BB requires AA. However it is possible for AA to be true even if BB is not true. We write
A⇐BA⇐BFor example, suppose AA is the statement “you sit the exam” and BB is the statement “you pass the exam”. You cannot pass the exam without sitting the exam: sitting the exam is a necessary condition for passing the exam. However sitting the exam does not mean that you will necessarily pass the exam.
Sufficient Condition
The statement AA is said to be a sufficient condition for the statement BB if knowing that AA is true guarantees that BB is also true. However knowing that BB is true does not guarantee that AA is true. That is, BB needn't be a sufficient condition for AA. We writeA⇒BA⇒BFor example, suppose AA is the statement “you achieve an overall grade of over 70%70% in all of the modules that you have studied as part of your economics degree” and BB is the statement “you get a first class degree in economics”. Achieving an overall grade of over 70%70% in all of the modules that you have studied as part of your economics degree means that you will get a first class in economics economics. However, getting a first class degree in economics does not necessarily mean that you achieved a first in all of your economics modules.
Necessary and Sufficient Condition
We say that the statement AA is a necessary and sufficient condition for the statement BB when BB is true if and only if AA is also true. That is, either AA and BB are both true, or they are both false. Note that if AA is necessary and sufficient for BB, then BB is necessary and sufficient for AA. We writeA⇔B.A⇔B.For example, the statement “I am a male sibling” is necessary and sufficient for the truth of the statement “I am a brother”.
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Some ‘Naiyayika’ scholar may try to explain the ‘Anvaya –Vyapti- Vyatireka’ in the modern example and see why the two concepts are related yet different.
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