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 n
umbers. 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)=
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)=
1 answer:
Draw a diagram representing the real number line, and the sets A and B.
According to the diagram:
<span>1. A∪B= [-7, 5)
2. </span><span>2. A∩B∩C= (-1, 0)
</span>3. A∩(B∪C)= [-7, 1] <span>∩ (-INFINITY, 5) = [-7, 1]
4. </span>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)
According to the diagram:
<span>1. A∪B= [-7, 5)
2. </span><span>2. A∩B∩C= (-1, 0)
</span>3. A∩(B∪C)= [-7, 1] <span>∩ (-INFINITY, 5) = [-7, 1]
4. </span>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)
You might be interested in