Check all that apply.

A statement with the form p $$ q is false if and only if p is true and q is false.

If the biconditional $($B $$ P$)($Z $$ F$)$ is false, then B $$ P and Z $$ F are both false.

In the statement ~$($M $$ X$)$~$)$ governs the simple statement M$.$

If B $$ P is true, then B $$ P must also be true.

If two statements have identical truth values, then the conjunction of those statements must be true.

A statement with the form p $$ q is true if either or both p and q is true.

A statement with the form p $$ q is true if and only if p and q are both true.

If A $$ C is false, and S $$ D is false, then the conditional $($A $$ C$)($S $$ D$)$ is true.

If C $$ Q is false and ~D $$ E is true, then the biconditional $($C $$ Q$)($~D $$ E$)$ is false.

The horseshoe $()$ operator perfectly captures the meaning of every ordinary language conditional statement.

The tilde $($~$)$ operator can apply only to a simple statement and never to a compound statement in parentheses.

A statement with the form p $$ q is false if and only if p is false and q is false.

Statement variables, which are used to represent statement forms, are lowercase letters $($p$,$ q$,$ r$,$ s$,$ and so on$).$

The horseshoe $()$ operator $($material conditional$)$ does not perfectly capture the meaning of all ordinary language conditional statements.

If K $$ M is true, then K $$ M must also be true.