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.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

no because mercury has a density of 13.6 grams per centimeter squared while gold has 19.32 grams centimeter squared

step-by-step explanation: