Question

chapter 1 quiz
score: 24/100 answered: 4/15
question 5
suppose that the universal set ( u ) is the set defined as ( u = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ).
write the sets ( a ) and ( b ) out in roster notation.
( a = {x in u mid x \text{ is an even number} } = { } )
( b = {x in u mid x \text{ is a prime number} } = { } )
find each of the following:
( n(a) = )
( n(b) = )

Explanation:

Step1: Determine set A (even numbers in U)

Even numbers are divisible by 2. From \( U = \{1,2,3,4,5,6,7,8,9,10\} \), the even numbers are 2, 4, 6, 8, 10. So \( A = \{2, 4, 6, 8, 10\} \).

Step2: Determine set B (prime numbers in U)

Prime numbers are greater than 1 and have no divisors other than 1 and themselves. In U, prime numbers are 2, 3, 5, 7. So \( B = \{2, 3, 5, 7\} \).

Step3: Find \( n(A) \) (number of elements in A)

Set A has 5 elements, so \( n(A)=5 \).

Step4: Find \( n(B) \) (number of elements in B)

Set B has 4 elements, so \( n(B)=4 \).

Answer:

\( A = \{2, 4, 6, 8, 10\} \)
\( B = \{2, 3, 5, 7\} \)
\( n(A) = 5 \)
\( n(B) = 4 \)