Where x<=0 with the usual operations in R^2 (a) If u and v are any elements in V

Question

Where x<=0 with the usual operations in R^2

(a) If u and v are any elements in V, then u + v is in V. (We say that V is closed under the operation +.)

(1) u + v = v + u for all u, v in V.

(2) u +(v + w) = (u + v) + w for all u, v, w in V.

(3) There exists an element 0 in V such that u + 0 = 0 + u = u for any u in V.

(4) For each u in V there exists an element u in V such that u + (u) = u + u = 0.

(b) If u is any element in V and c is any real number, then c u is in V (i.e., V is closed under the operation ).

(5) c (u + v) = c u + c v for any u, v in V and any real number c.

(6)(c + d) u = (c u) + (d u) for any u in V and any real numbers c and d.

(7) c (d u) = (cd) u for any u in V and any real numbers c and d.

(8) 1 u = u for any u in V.

(9) None of the above

Explanation / Answer

The answer is 4, b

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