Question

Consider the intervals A= [1, -1), B= (0, 2), C= [0, 3). Show that (A ∪ B) ⊄ C.

Answer 1

In the Above Question Given Intervals are

A=[1,-1) => Range of integers from 1 to -1 with 1 inclusive and -1 exclusive since [] denotes closed interval and () denotes open interval

  i.e.1,0,-0.5  

B=(0,2) => Range of integers from 0 to 2 with 0 exclusive and 2 exclusive since [] denotes closed interval and () denotes open interval

i.e.0.5,1,1.5

C=[0,3) => Range of integers from 0 to 3 with 0 inclusive and 3 exclusive since [] denotes closed interval and () denotes open interval     

i.e.0.5,1,1.5,2,2.5

Also,(A U B) contains values present in both A and B

i.e.-0.5,0,1,1.5

But, C doesn't contain -ve numbers.

Hence (A U B) ⊄ C .Proof By observation.