Question

Consider the universal set R,R, define the interval A=[−7,1],A=[−7,1], interval B=(−1,5),B=(−1,5), and CC be the negative real numbers. Complete the following exercises in interval notation.

1. A∪B=A∪B=

2. A∩B∩C=A∩B∩C=

3. A∩(B∪C)=A∩(B∪C)=

4. A^c ∪ B^c∪ C^c=

5. (C−A)∪(B−C)=(C−A)∪(B−C)=

Answer 1

Draw a diagram representing the real number line, and the sets A  and B.

According to the diagram:

1. A∪B= [-7, 5)

2. 2. A∩B∩C= (-1, 0)

3. A∩(B∪C)= [-7, 1] ∩ (-INFINITY, 5) = [-7, 1]

4. 4. A^c ∪ B^c∪ C^c= (not A) ∪ (not B) ∪ (not C) = 

(-infinity, -7) ∪ (1, infinity)   ∪  (-infinity, -1] ∪ [5, infinity)   ∪ [0, infinity)

= (-infinity, -1] ∪ (1, infinity ) ∪ [0, infinity) = (-infinity, -1] ∪ [0, infinity) 

5. (C−A)∪(B−C)= "in C but not in A" union "in B but not in C"

=(-infinity, -7) ∪ [0, 5)