This Statement is Tralse. Wait What?
Out of the 8 statements below, how many is/are true?
(A)
At least 1 of these statements is true.
(B)
At least 2 of these statements are true.
(C)
At least 3 of these statements are true.
(D)
At least 4 of these statements are true.
(E)
At least 5 of these statements are false.
(F)
At least 6 of these statements are false.
(G)
At least 7 of these statements are false.
(H)
At least 8 of these statements are false.
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1 solution
The first thing that should strike your head is that H must be tralse... I mean... false. :D
Let's assume G is true, then A is true, but this contradicts G as now there are only at most 6 statements that can be false. Hence, G must be false.
Next let's assume F is true, then A is true, which then implies B is true, which in turn implies C is true, which again in turn implies D is true, but this contradicts F since 5 of them are already true. Hence, F must be false.
The same goes for E , as if E is true, A , B , C and D must all be true, this contradicts E , thus E must be false.
Now since E is false, A , B , C and D must all be true, because if it isn't, then at least 5 of the statements are false, this contradicts E . When A , B , C and D are all true, they all satisfy the situation.
Hence, A , B , C , D are true while E , F , G , H are false, the number of statements that are true is 4.