The given set together with the given operations is not a vector space. List the

Question

The given set together with the given operations is not a vector space. List the properties of the definition that fail to hold. (Select all that apply.)
The set of all ordered pairs of real numbers with the operations
(x, y) (x', y') = (x + x', y + y')
and
r (x, y) = (x, ry).
(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.
None of the above

Explanation / Answer

the answer is just 6

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