Graph sets A and B and find the sets given by the different options.
C
Practice makes perfect
Let's first graph both sets on a number line. To graph A, we place an open dot at - 1 and shade everything to the right.
To graph set B, we shade everything between - 3 and 2, inclusive.
Option A
The statement A⋃ B={ } says that the union of set A and B is empty. However, since neither A nor B are empty sets, their union will not be an empty set either. The statement cannot be true.
Option B
A' is the complement set to A which describes everything that is not included in A. If A contains all numbers greater than - 1, the complement to A must contain all numbers less than or equal to - 1.
We can write set A' as:
A'={x | x≤ - 1},
which does not perfectly match the statement. Hence, B is also not correct.
Option C
Aâ‹‚ B is the intersection of A and B, which describes the elements that are shared by the sets. In other words, it is the segment on the number line that belongs to both sets. Let's find it below.
The intersection of A and B is then all elements starting from, but not including, - 1 and up to 2, inclusive. We can write this as below:
Aâ‹‚ B={x | - 1
Option D
The sign ⊆ means that all elements of B should be contained in the set {x | x<2}. Let's first graph this set by placing an open dot at 2 and then shade everything to the left of it.
As we can see, the green set does not contain 2 while B does, so the statement is not correct.
