- #1

johnsmiths

- 4

- 0

## Homework Statement

find a logical expression using only ∧ and ¬ operators which is logically equivalent to (p ∨ q)

## The Attempt at a Solution

losing direction

what should I first consider?

There is another question about recurrent relation.

Suppose that a mathematical expression can only be formed by the following symbols: 0, 1,

2, …, 9, ×, +, /. Some examples are “0 + 9”; “2 + 2 × 8”; “1 / 5 + 6”. Let an be the the number

of such mathematical expression of length n (e.g. “0 + 9” is considered of length 3). Find a

recurrence relation for an and compute the closed form for a

_{n}.

[Some clarification: We define a number as follows

- 0, 1, 2, …, 9 is a number

- If x is a number, then x0, x1, …, x9 is a number

We define a valid expression as follows

- E is a valid expression if E is a number

- If E, F are valid expressions, then E + F, E × F, E / F are also valid expressions.

For example: 1+50/4 is an expression of length 6, and 09×00/5 is an expression of length 7.]

Totally no idea about this question.