Answer to Question #93019 in Discrete Mathematics for Unknown287159

Question

1. Let x = (1,2,3,4), Y = (2,3,5) and Z =(4,5,6). verify the following:
a) x U y = y U x.
b) (x U y) U z = x U (y U z).

Answer 1

a) x U y = (1,2,3,4) U (2,3,5) = (1,2,3,4,5).

y U x = (2,3,5) U (1,2,3,4) = (1,2,3,4,5).

So, x U y = y U x.

b) (x U y) =(1,2,3,4,5), (x U y) U z = (1,2,3,4,5) U (4,5,6) = (1,2,3,4,5,6).

y U z = (2,3,5) U (4,5,6) = (2,3,4,5,6), x U (y U z) = (1,2,3,4) U (2,3,4,5,6) = (1,2,3,4,5,6).

So, (x U y) U z = x U (y U z)