Question

Express the given circuits in symbolic form.

Answer 1

Hint: A sentence written in symbolic form uses symbols and logical connectors to represent the sentence logically. Symbolic logic is used to represent logical expressions by using symbols and variables in place of natural language. There are many expressions that we can prove that are either true or false.

Complete step-by-step solution:

A switching circuit is the connection of a finite number of switches \[{S_1},{S_{2,}}{S_1}',{S_2}'\] the question under consideration being whether electric current will flow in the circuit for a given situation of the switches or not. There are only two possibilities for any switch: it is either on or off.
In any type of circuit, there are only two possibilities: either the current flows through it or not. When the circuit is closed, the current that is flowing through it is called on. Same as if the circuit is open, the current is not flowing and the circuit is off.
Let,
\[p\]: The switch \[{S_1}\] is closed
\[q\]: The switch \[{S_2}\]is closed
\[\neg p\]: \[{S_1}'\] means the switch is closed or the switch \[{S_1}\]is open
\[\neg q\]:\[{S_2}'\] means the switch is closed or the switch \[{S_2}\]is open
 The symbolic form of the given circuit is:
\[\left( {p \wedge q} \right) \vee \left( {\neg p} \right) \vee \left( {p \wedge \neg q} \right)\]
Where,
\[p,q\]- Statements
\[ \vee \] - Or
\[ \wedge \] - And
\[\neg \]- It is not the case that.

Note:The symbolic logic, a letter such as\[p,q\] stands for an entire statement…
In symbolic logic, a sign such as \[ \vee \] connect the two statements to form a third statement.
This symbol”\[ \vee \]” replaces the word "or".
This symbol”\[ \wedge \]” replaces the word "and."