Mathematical Logic

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

Which of the following compound statements is a tautology?

Find the statement which is logically equivalent to the given statement

$~(~p\to q)$

State Absorption law. Construct the truth table for the following statement.

$\left(p\vee q\right)\vee \neg q$.

State Absorption law. Construct the truth table for the following statement.

$\left(\neg p\to r\right)\wedge \left(p\leftrightarrow q\right)$.

State Absorption law. Show that $\neg \left(p\to q\right)\equiv \left(p\wedge \neg q\right)$

Prove Absorption law i.e. $p \mathrm{or} (p \mathrm{and} q)=p$

Prove Absorption law i.e. $p \mathrm{and} (p \mathrm{or} q)=p$.

Using the truth table examine whether $\left[\right(p\vee ~q)\vee (~p\wedge q\left)\right]\wedge r$ is tautology, contradiction or contingency.

Using the truth table examine whether $(p\vee q)\wedge (p\vee r)$ is tautology, contradiction or contingency.

Using the truth table examine whether $(p\wedge q)\vee (p\wedge r)$ is tautology, contradiction or contingency.

Using the truth tables, examine whether the given statement $(p\wedge q)\to r$ is tautology, contradiction or contingency.

Using the truth tables, examine whether the given statement $(p\vee q)\wedge ~p$ is tautology, contradiction or contingency.

Draw the simplified switching circuit for the following switching circuit.

Give an alternate arrangement for the circuit, so that the new circuit has two switches only.

Define an open statement. Find the truth value of open statement $3x=9$ at $x=3$.

Define an open statement. Find the truth value of open statement $3x=9$ at $x=2$.

Define an open statement. Find the truth value of open statement $x^2+2=11$ at $x=-3$.

Define an open statement. Find the truth value of open statement $x^2+2=5$ at $x=1$.

Find the conclusion in the following conditional statement.

If Earth is more closer to Sun, then it is more hotter.