Answers: 36) 1 & 4 37) 16 38) 38 39) 16
Explanation:
Notes:
U = 3 ≤ x < 14, x ∈ N
means that everything within the rectangular box (including the circles) contains the Natural Numbers of 3 through 14, including 3 but excluding 14.
R = 5 ≤ x ≤ 8, x ∈ N
means that everything within the circle of R (including the intersection with T) contains the Natural Numbers of 5 through 8, including 5 and 8.
T = {4, 7, 10, 13}
means that everything within the circle of T (including the intersection with R) contains 4, 7, 10, & 13.
Filling in the Venn Diagram:
R (only) contains 5, 6, 8
R∩T (the middle section of R and T) contains 7
T (only) contains 4, 10, 13
outside the circles but inside the rectangle (usually written on the lower left corner) is 3, 9, 11, 12
Statements:
1) R ∩ T = {7}
means the intersection of R and T (the middle circle) contains 7 and nothing else.
Refer to your Venn Diagram. This statement is TRUE!
2) n(R ∪ T)' = 6
means the QUANTITY of numbers NOT in both R & T is 6.
The numbers that are not in either R or T are: 3, 9, 11, 12.
That results in 4 numbers (not 6). This statement is False.
3) n(R' ∩ T) = 2
means the QUANTITY of numbers that are NOT in R but are in T is 2.
The numbers that are not in R but are in T are: 4, 10, 13.
That results in 3 numbers (not 2). This statement is False.
4) n(R ∩ T') = 3
means the QUANTITY of numbers that are in R but NOT in T is 3.
The numbers that are in R but NOT in T are: 5, 6, 8.
That results in 3 numbers. This statement is True!
Filling in the 2nd Venn Diagram:
A = 11; middle section = 13; B = 14, outside of circles = 2
37) (A') means NOT in A: 40 - 24 = 16
38) (A ∪ B) means all of the numbers in both A and B: 24 + 27 - 13 = 38
39) (A' ∪ B) means NOT in A and includes all in B: 40 - 24 = 16