relational expression, zermelo definition, proper divisor...

Q) [/B]Consider the predicate D : N × N → {T, F} (N stands for the natural numbers)

where D(x, y) means ‘x is a proper divisor of y’.

(a) Write a boolean expression for D(x, y), using relational expressions and

boolean operators.

(b) Let E be the set of even natural numbers which are greater than 2.

1. Define E with words, using the expression ‘proper divisor’.

2. Give the Zermelo definition of E, using the predicate D.

(c) Write the Zermelo definition of each of the following sets, using the predicate D and a quantifier in each case.

1. The set of prime numbers.

2. The set of composite natural numbers.

3. The set of natural numbers greater than 1.