Question

Which of the following logical expressions describes the scope of (x in N) in the given statement: ((x in N, f(x) = 5) land (y in N, f(y) < 5))?

a) Elements in set N satisfying (f(x) = 5) and (f(y) < 5)
b) Elements in set N satisfying (f(x) = 5) only
c) Elements in set N satisfying (f(y) < 5) only
d) Elements in set N satisfying (f(x) = 5) or (f(y) < 5)

Answer 1

The scope of (x in N) in the statement provided pertains only to the part where f(x) = 5, as x and y are distinct elements represented by different variables.

Step-by-step explanation:

The correct answer to the question 'Which of the following logical expressions describes the scope of (x in N) in the given statement: ((x in N, f(x) = 5) land (y in N, f(y) < 5))?' is b) Elements in set N satisfying (f(x) = 5) only. As the logical expression uses the logical AND (land) operator, it means that we are considering the elements for which both conditions must be true. However, since x and y are different elements (as implied by their different notations), the scope of x is only the part of the statement where it is mentioned, i.e., where f(x) = 5. So, the 'land' does not mean that x must also satisfy f(y) < 5; that part pertains only to y.