Let
For every
a. Draw arrow diagrams for U, V, and W.
b. Indicate whether any of the relations U, V, and Ware functions.
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- Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.arrow_forward3. Let a e Z, b E Z. Find f(3,9), ƒ (17, 2), ƒ(6, 4), where f(a,b) is defined by: if a b.arrow_forwardLet C denote the set of all ordered pairs (a, b) with a,b & R. L.e., C:= {(a,b): a, b = R}. Define addition + and multiplication of such pairs by (u, v) + (x, y) = (u + x, v+y) and (u, v) • (x, y) = (ux — vy, uy + vx) R. Together they form a triple . for all u, v, r, y (a) Show that multiplication is associative in . (b) Show that every element (a, b) € C has a negative, and every element (a, b) € C# has an inverse. (c) Prove or disprove: The system of real numbers R is isomorphic to the system . Here, 0 R is the zero of R. (d) True or false? Justify your answer: The triple C, +, > must contain a subfield isomorphic to R.arrow_forward
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