Question

S is a set of arithmetic expressions as strings recursively defined as follows.

Base case: Every variable from the set { a, b, c, d, e, f } is in S.
Recursive rules: If x ∈ S and y ∈ S, then: 1. (x + y) ∈ S 2. x • y ∈ S
Indicate which expressions are in S.
1. (x + y) Є S
2. x.y Є S

Indicate which expressions are in S.
O (a + b + c)
O (ad) + (c.b)
O (a + d) • (e +f) .
O a•b

Answer 1

The set of arithmetic expressions S is defined recursively. All the expressions listed are in S.

Step-by-step explanation:

The set of arithmetic expressions S is defined recursively. The base case states that every variable from the set { a, b, c, d, e, f } is in S. The recursive rules specify that if x ∈ S and y ∈ S, then (x + y) ∈ S and x • y ∈ S. To indicate which expressions are in S, we can analyze each expression according to these rules:

1. (x + y) ∈ S
2. x.y ∈ S (x • y)

In this case, all the expressions listed are in S.