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]

show work,

a. (1,6]

b. (4,6]

c. [2,4)

d. (2,6]

show work,

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

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

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