Question

Which of the following intervals represents the set (1,4) u [2,6]?

a. (1,6]
b. (4,6]
c. [2,4)
d. (2,6]

Please show work,

Thanks!

Answer 1

Set is a sum of two intervals :(1,4) u [2,6]
In the first interval it is open on both sides so 1 and 4 don't belong to this interval, the second is closed so both 2 and 6 belong to interval and numbers between 2 and 6
We can write it as 1<x
`\leq 6`
summing both sets we have one set: (1,6]
so
a) represent our set
b) also represent because all numbers between 4-6 and 6 are in our set
c)also represent, all numbers are in main set
d)also represent

Answer 2

`(1;\ 4)\ \cup\ [2;\ 6]=(1;\ 6]\\\\Answer:A.`