Define a Set $S$ Recursively as Follows:
I $\epsilon \in S$ II RECURSION: If

question 20

Essay

Define a set $S$ recursively as follows:
I. BASIS: $\epsilon \in S$
II. RECURSION: If $s$ and $t$ are in $S$ , then
$\begin{array} { l l l l } \text { a. } 0 s \in S & \text { b. } s 0 \in S & \text { c. } 1 s 1 t \in S & \text { d. } s 1 t 1 \in S \end{array}$
III. RESTRICTION: No strings other than those derived from I and II are in $S$ . Use structural induction to prove that every string in $S$ contains an even number of l's.

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Definitions:

Output PL1

Denotes an output signal or data in the first programming language (PL/I), commonly used in control systems or programming.

Energized

A state in which a component, circuit, or system is supplied with electrical power, causing it to be active or in a working state.

Masked Move Instruction

An instruction in computer programming that selectively modifies bits in a destination operand based on a mask operand.

Output Instruction

The term applied to any programmable logic controller instruction capable of controlling the discrete or analog status of an output device connected to the programmable logic controller.