25 statements
I have 25 statements
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If , then .
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If not , then not .
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If , then .
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If not , then not .
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If , then .
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If not , then not .
...
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If , then .
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If not , then not .
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If , then .
What can we conclude from all statements above?
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1 solution
The contrapositive of any logically true statement is always true.
Hence, "If not C , then not B " is equivalent to "If B , then C ;" "If not E , then not D " is equivalent to "If D , then E ;" and so on.
Thus, we have a series of statements that, following a sort of transitive property for logically true statements, reduce to "If A , then Z ," whose contrapositive is "If not Z , then not A ."
"If Z , then A " cannot be concluded because the converse of a logically true statement is not necessarily true.
Regarding the other 2 options, we cannot conclude anything about A and Z , individually, because the essence of "if, then" statements is that the truth of the conclusion is dependent on truth of the premise.