Algebra of Statements

State whether the following conditions are true or false.

$~T\equiv F, ~F\equiv T \&\hspace{0.17em}~\left(~P\right)\equiv P$

State whether the following statement is true or false.

$p \vee ~p = T \& p \wedge ~p=F$

Select the associative law of statements from the following.

$0$ is idempotent under multiplication.

State whether the following statement is true or false.

The dual of a compound proposition that contains only the logical operators $\wedge , \vee \& \neg$ is the compound proposition obtained by replacing each $T by F$.

State whether the following statement is true or false.

The dual of a compound proposition that contains only the logical operators $\wedge , \vee \& \neg$ is the compound proposition obtained by replacing each $\vee by \wedge$.

State whether the following statement is true or false.

The $P\to Q$ and $\neg P\vee Q$ relations are logically equivalent.

Show that $P\to Q$ and $\neg P\vee Q$ are logically equivalent.

What is the distributive law with "or"?

Consider $a, b \& c$ be the three statements.

What is the distributive law with "and"?

Consider $a, b \& c$ be the three statements.

What is the identity law with "or"?

For any statement $a$.

What is the identity law with "and"?

For any statement $a$.

What is the commutative property with "or"?

If $a \& b$ are three statements.

What is the commutative property with "and"?

If $a \& b$ are three statements.

The true value of the _____ of two statements is completely determined by the truth value of its conjuncts.

A conjunction is true if and only if 

Which one of the following is logically equivalent to $\left(P\vee Q\right)\wedge \left(~P\right)\Rightarrow Q$

Find the statement which is logically equivalent to the given statement

$~(~p\to q)$

The compound statement $\left(P\vee Q\right)\wedge \left(~P\right)\Rightarrow Q$ equivalent to:

Which of the following is logically equivalent to $~\left(p\wedge q\right)$?