Answer: Using union and intersection of sets the answers are:
1. Option D. {red pen, blue pen, green pen, yellow pen, black pen}
2. Option B. {walnuts, peanuts, pistachios, pecans, almonds, Brazil nuts}
3. Option A. {0,3,6,9,12}
4. Option B. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14}
5. Option D. {fever, joint pain, tiredness}
Solution:
1. You have two boxes of colored pens. The first box contains a red pen, a blue pen, and a green pen:
Box 1: B1 = {red pen, blue pen, green pen}
The second box contains a yellow pen, red pen, and a black pen:
Box 2: B2 ={yellow pen, red pen, black pen}
What s the set that represents all the pens?
This set is the union (U) of the two sets, that means the elements of the two sets (the repeated elements are written only once):
B1 U B2 = {red pen, blue pen, green pen} U {yellow pen, red pen, black pen}
B1 U B2 = {red pen, blue pen, green pen, yellow pen, black pen}
This is option D.
2. The bulk food section of a grocery store has two bins with different types of mixed nuts. The first bin contains walnuts, peanuts, and pistachios:
Bin 1: B1 = {walnuts, peanuts, pistachios}
The second bin contains pecans, almonds, Brazil nuts, and walnuts:
Bin 2: B2 = {pecans, almonds, Brazil nuts, walnuts}
What is a set that represents all the types of nuts in the bins?
This set is the union (U) of the two sets, that means the elements of the two sets (the repeated elements are written only once):
B1 U B2 = {walnuts, peanuts, pistachios} U {pecans, almonds, Brazil nuts, walnuts}
B1 U B2 = {walnuts, peanuts, pistachios, pecans, almonds, Brazil nuts}
This is option B.
For questions 3-4, let X= {x | x is a whole number less than 15}, Y={x | x is a multiple of 3 less than 15}, Z= {x | x is a real number greater than or equal to 5.5}.
X= {x | x is a whole number less than 15}
whole number < 15: 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14
X={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14}
Y={x | x is a multiple of 3 less than 15}
multiple of 3 < 15: 0,3,6,9,12
Y={0,3,6,9,12}
3. What is X ∩ Y?
X ∩ Y is the set formed by the common elements of X and Y
X ∩ Y = {0,3,6,9,12}
This is option A.
4. What is X U Y?
X U Y is the union (U) of the two sets, that means the elements of the two sets (the repeated elements are written only once):
X U Y = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14}
X U Y = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14}
This is option B.
5. A doctor is examining three patients. Which symptoms do all three patients have in common?
This is the intersection of sets formed by the symptos of the three patients. According with the graph, the common area between the three sets contains the elements fever, tiredness, and joint pain.
This is option D. {fever, joint pain, tiredness}
