∀x∀y(((x ≥ 0) ∧ (y < 0)) → (x – y > 0))
A. A non-negative number - a negative number is positive.
B. For any two real numbers, the first is non-negative, the second is negative, and the difference is positive.
C. For every non-negative number, one can find a negative number so that the first number minus, the second is positive.
D. One can find a non-negative number and a negative number so that the first minus, the second is positive.
E. One can find a non-negative number so that for any positive number chosen, the first number minus, the second is positive.

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MrRoyal MrRoyal · Answer 1 · 2020-11-29T16:26:46+01:00

Answer:

B. For any two real numbers, the first is non-negative, the second is negative, and the difference is positive.

Step-by-step explanation:

To answer this question, I'll analyse the mathematical statements one at a time

The analysis is as follows:

∀x -> This means real number x

∀y -> This means real number y

(x ≥ 0) -> Such that real number x is greater than or equal to 0. In other words, x is positive

∧ -> and

(y < 0)-> y is less than 0. In other words, y is negative

So, there are two real numbers: x and y

→ (x – y > 0) -> Their difference is greater than 0. In other words, their difference is positive

When the analysis above is compared to the list of given options; the option that match is B.

Hence, option B answers the question.