Characterizing the strings in a recursively defined set.

the recursive definition given below defines a set s of strings over the alphabet {a, b}:

base case: λ ∈ s and a ∈ s

recursive rule: if x ∈ s then,

xb ∈ s (rule 1)

xba ∈ s (rule 2)

(a)

use structural induction to prove that if a string x ∈ s, then x does not have two or more consecutive a's.

y > 1/3x

y < = -x + 4

hope this : )

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.

e

step-by-step explanation:

an equation by definition has to have two or more variables (x and 2 in this case)

the answer to your question is c.)   volcanoes built the mountains and earthquakes tore them down.

step-by-step explanation: