Let P denote the set of primes and E the set of even integers. As always, Z and N denote the integers and natural numbers, respectively. Find equivalent formulations of each of the following statements using the notation of set theory that has been introduced in this section. (a) 0 is an integer but not a natural number.

{0} ∈ Z ∧ {0} ∉ N

Step-by-step explanation:

The notations we can use here are:

∈ = belongs

∉ = does not belong.

∧ = and

So, if we want to say that 0 is an integer, we use:

{0} ∈ Z

if we want to say that 0 is not a natural number, we use:

{0} ∉ N

And, if we want to say both in the same statement, we can use the "and" symbol:

{0} ∈ Z ∧ {0} ∉ N