Question

Consider the following sets. The universal set for this problem is N. A = The set of all even numbers. B - The set of all prime numbers. C-The set of all perfect squares. DThe set of all multiples of 10. Using only the symbols 3. A. B. C. D. N. . S.-f.n U.. 0.and). write the following statements in set notation.'. is complement set) (a)None of the perfect squares are prime numbers. (b)All multiples of 10 are even numbers. (c) The number 3 is a prime number that is not even. (d)If you take all the prime numbers, all the even numbers, all the perfect squares, and all the multiples of 10, you still won't have all the natural numbers.

Answer 1

In set notation:

Step-by-step explanation:

a. None of the perfect squares are prime numbers can be written as A ∩ B' = ∅. This means that there are no elements that are common to the set of perfect squares and the complement of the set of prime numbers. Therefore, none of the perfect squares are prime numbers.

b. All multiples of 10 are even numbers can be written as D ⊆ A. This means that all elements in the set of multiples of 10 are also in the set of even numbers. Therefore, all multiples of 10 are even numbers.

c. The number 3 is a prime number that is not even can be written as 3 ∈ B' ∩ A'. This means that the number 3 is an element in both the complement of the set of prime numbers and the complement of the set of even numbers. Therefore, the number 3 is a prime number that is not even.

d. If you take all the prime numbers, all the even numbers, all the perfect squares, and all the multiples of 10, you still won't have all the natural numbers can be written as (A ∪ B ∪ C ∪ D) ≠ N. This means that the union of the sets A, B, C, and D is not equal to the universal set N. Therefore, taking all the prime numbers, even numbers, perfect squares, and multiples of 10 will not give you all the natural numbers.