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Stoolfi u only proved that for +ve values it suffices but not for -ve values, so u can say that B is sufficient only if its true for both +ve and -ve values but in this case its not. So I think B is not sufficient. What do u say?

B tells us, as I have shown, that x is a positive number that is less than 1.

1 will always be greater than all numbers less than 1, by definition.

You contend that I "only proved that for +ve values it suffices but not for -ve values", but B says that x is positive. In other words, there are no negative values of X that make B true.

I just came up with one other method of answering, by drawing graphs.

the first eq, x^2<1, is a U shaped graph and for all values of x<1, y<1 too. So, A is correct.

For the second eq, |x|<1/x, draw two graphs, y=|x|, which is a 45 degree straight line hinged at (0.0) making a V.
y=1/x is an inverse of y=x.
For all values of graph 1 < graph 2, |x|<1. So, B is correct as well.