Find the component statements of the following compound statement:
All rational numbers are real and all real numbers are complex.

$(p \wedge \sim q) \wedge (\sim p \vee q)$ is

The statement pattern $(p \land q) \to (r \lor \sim s)$ is false. Then the truth values of $p, q, r$ and $s$ are respectively

For the simple statements $p, q$,and $r$,$p \rightarrow (q \vee r)$ is logically equivalent to

Among the statements:
$(S1) \quad (( p \vee q )$ $\Rightarrow r ) \Leftrightarrow ( p$ $\Rightarrow r )$
$(S2) \quad (( p \vee q )$ $\Rightarrow r ) \Leftrightarrow (( p$ $\Rightarrow r ) \vee ( q$ $\Rightarrow r ))$

Identify the type of "Or" used in the following statement and check whether the statement is true or false:
To enter into a public library,children need an identity card from the school or a letter from the school authorities.