Doubts on Sufficient vs Neccessary Conditionals (help)
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04 Nov 2023, 03:36
Hello,
I am trying to learn the neccessary vs sufficient condition, but different sources have contradictory information on this topic.
I will list what I know,
Statement: If P, then Q
P -> Q
P = sufficient condition
Q = Neccessary condition
Contrapositive: If not Q, then not P
~Q = Sufficient condition (where ~ mean the negative/opposite)
~P = Neccessary condition
~P > ~ Q
P unless Q (or Unless Q, P)
P = sufficient condition
Q = Neccessary condition
translating Unless to If-then results in:
If not P then Q
Example1:
Unless you try (Q) , you won't succeed (P).
P (You will succeed) = sufficient condition (negated)
Q (trying) = Neccessary condition
Translating unless to If-then results in:
If you don't try, then you won't succeed
However, I found another example which contradicts this translation of Unless to If-then:
Maria will not speak during the meeting (P) unless the chairman does not speak (Q).
P (Maria WILL speak) = sufficient condition (negated)
Q (Chairman does not speak) = neccessary condition
~P -> Q
Translating unless to if-then results in:
If Marie speaks, then the chairman will not speak.
If ~P , then Q
To generalise:
P unless Q
becomes:
If not P, then Q.
Please let me know if what is in red is correct.