Hello every one
In the following example, I have a really problem to understand the third and thr fourth cases : May someone add explanation please and thank you ?
"If exactly one of these statements is false, which statement is false?
A. Statement D is true. B. Statement A is false. C. Statement B is false. D. Statement C is true.
Since one of the statements is false, it suffices to consider 4 cases, each case assuming one of statements to be false and then checking if this assumption is consistent with other statements or not.
Case 1: Statement A is false. This implies Statement D is false. Since no more than one statements can be false, this assumption is wrong.
Case 2: Statement B is false. This leads to conclusion that A is true, D is true, and C is true. (Looks good)
Case 3: Statement C is false. This results in conclusion of truthfulness of B, and thus fallacy of A, which is not possible.
Case 4: Statement D is false. It signifies that C is false, which is invalid.
So the statement which is wrong is Statement B." □