> 2. Only conclusion 1 is necessarily true, because of the transitive property of inequalities; X ? Y and Z/Y can be rewritten as X < Y <= Z. However, we cannot relate any magnitude information to V and it is not necessarily true that a number becomes larger when multiplied by another number (if we assume X is zero and V is positive, for instance).
It says that the product of X and V is greater than or equal to the sum of X and V. Conclusion 2 is that the sum of X and V is less than the product of X and V. How could the latter claim be false if the former premise is true?
I agree with you on 4 and came to it another way: 3^3 : 3 * (3-1) * (3+1) :: 4^3 : 4 * (4-1) * (4+1)
> It says that the product of X and V is greater than or equal to the sum of X and V. Conclusion 2 is that the sum of X and V is less than the product of X and V. How could the latter claim be false if the former premise is true?
Suppose X is 0 and V is 0. The product of X and V is 0 which is indeed less than or equal to 0 - 0 = 0. Substituting V and X both for zero in (V - X) < (V * X) gives us (0 - 0) < (0 * 0) which simplifies to 0 < 0, which is false.
It says that the product of X and V is greater than or equal to the sum of X and V. Conclusion 2 is that the sum of X and V is less than the product of X and V. How could the latter claim be false if the former premise is true?
I agree with you on 4 and came to it another way: 3^3 : 3 * (3-1) * (3+1) :: 4^3 : 4 * (4-1) * (4+1)
4 * 3 = 12 * 5 = 60