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Algebra of Statements is considered one the most difficult concept.
79 Questions around this concept.
Which statement is most precise about logic?
Which of the following is NOT a type of sentence ?
Which of the following is NOT assertive statement ?
Which of the following is not a simple statement?
Which of the following sub statements can form a compound statements ?
Which of the following statements does not have a conjugative ?
Which one is NOT an example of an AND conjunction?
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Which of the following is not a disjunction ?
What is negation of x > 5 ?
The contrapositive of the statement ‘If two numbers are not equal, then their squares are not equal’, is :
Idempotent Law
1. $p \vee p \equiv p$
2. $p \wedge p \equiv p$
$
\begin{array}{|c|c|c|}
\hline p & p \vee p & p \wedge p \\
\hline \hline \mathrm{~T} & \mathrm{~T} & \mathrm{~T} \\
\hline \mathrm{~F} & \mathrm{~F} & \mathrm{~F} \\
\hline
\end{array}
$
Associative Law
1. $(p \vee q) \vee r \equiv p \vee(q \vee r)$
2. $(p \wedge q) \wedge r \equiv p \wedge(q \wedge r)$
Distributive Law
1. $p \wedge(q \vee r) \equiv(p \wedge q) \vee(p \wedge r) \mid$
2. $p \vee(q \wedge r) \equiv(p \vee q) \wedge(p \vee r)$
Commutative Law
1. $p \vee q \equiv q \vee p$
2. $p \wedge q \equiv q \wedge p$
Identity Law
1. $p \wedge T \equiv p$
2. $p \wedge F \equiv F$
3. $\mathrm{p} \vee T \equiv T$
4. $p \vee F \equiv p$
$
\begin{array}{|c|c|c|c|c|c|c|}
\hline p & T & F & p \wedge T & p \wedge F & p \vee T & p \vee F \\
\hline \hline \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~T} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} \\
\hline \mathrm{~F} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~F} \\
\hline
\end{array}
$
Complement Law
5. $p \vee \sim p \equiv T$
6. $p \wedge \sim p \equiv F$
7. $\sim(\sim p) \equiv p$
8. $\sim T \equiv F$
9. $\sim \mathrm{F} \equiv \mathrm{T}$
$
\begin{array}{|c|c|c|c|c|c|}
\hline p & \sim p & p \vee \sim p & T & p \wedge \sim p & F \\
\hline \hline \mathrm{~T} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} \\
\hline \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} \\
\hline
\end{array}
$
De-Morgan's Law
1. $\sim(p \vee q) \equiv \sim p \wedge \sim q$
2. $\sim(p \wedge q) \equiv \sim p \vee \sim q$
Truth table for $\sim(p \vee q)$ and $\sim p \wedge \sim q$
$
\begin{array}{|c|c|c|c|c|c|c|}
\hline p & q & \sim p & \sim q & p \vee q & \sim(p \vee q) & \sim p \wedge \sim q \\
\hline \hline \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} \\
\hline \mathrm{~T} & \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} \\
\hline \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} \\
\hline \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} \\
\hline
\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|}
\hline p & q & \sim p & \sim q & p \wedge q & \sim(p \wedge q) & \sim p \vee \sim q \\
\hline \hline \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} \\
\hline \mathrm{~T} & \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} \\
\hline \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} \\
\hline \mathrm{~F} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} & \mathrm{~F} & \mathrm{~T} & \mathrm{~T} \\
\hline
\end{array}
$
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