Question

What is special about the parentheses in the given expression: ( exists x in mathbb(Z), (exists k in mathbb(Z), 10 = kx) land (exists k in mathbb(Z), 100 = kx) )?

a) They indicate a set of integers
b) They denote a conditional statement
c) They represent the existence of a solution for two equations simultaneously
d) They separate the domain of x from the domain of k

Answer 1

The parentheses in the given expression denote the existence of a solution for two equations simultaneously, and they separate the existential statements regarding the variable x and k to show that a solution exists within the set of integers.

Step-by-step explanation:

The special quality of the parentheses in the given expression ( exists x in mathbb(Z), (exists k in mathbb(Z), 10 = kx) land (exists k in mathbb(Z), 100 = kx) ) is that they represent the existence of a solution for two equations simultaneously, where x and k are both integers. This is denoted by the notation exists, which is used to express that there is at least one integer value of x and k that can satisfy each equation, 10 = kx and 100 = kx, individually.

The use of parentheses separates the different existential statements, making it clear that for each part of the expression, a potentially different value of k may satisfy the equation. The statement as a whole indicates that there is some integer x which is a common factor of both 10 and 100.