25 statements

Logic Level 3

I have 25 statements

  • If A A , then B B .

  • If not C C , then not B B .

  • If C C , then D D .

  • If not E E , then not D D .

  • If E E , then F F .

  • If not G G , then not F F .


  • If W W , then X X .

  • If not Y Y , then not X X .

  • If Y Y , then Z Z .

What can we conclude from all statements above?

A A and not Z Z A A or not Z Z If Z Z , then A A If not Z Z , then not A A .

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1 solution

Zach Abueg
Jul 22, 2017

The contrapositive of any logically true statement is always true.

Hence, "If not C C , then not B B " is equivalent to "If B B , then C C ;" "If not E E , then not D D " is equivalent to "If D D , then E 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 A , then Z Z ," whose contrapositive is "If not Z Z , then not A A ."

"If Z Z , then A 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 A and Z Z , individually, because the essence of "if, then" statements is that the truth of the conclusion is dependent on truth of the premise.

For the sake of completeness, you have to show that all other options are false.

Zee Ell - 3 years, 10 months ago

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Thanks Zee, I've added such an analysis. What do you think?

Zach Abueg - 3 years, 10 months ago

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