5 views

Which one of the following propositional forms is tautology?

1. $p\ \wedge \sim (q\wedge p)$
2. $p\ \wedge \sim q$
3. $p\ \Rightarrow (p\wedge q)$
4. $p\ \Rightarrow (p\vee q)$
in Others | 5 views

1. $p\ \wedge \sim (q\wedge p)$ $\equiv$ $p\ \wedge (\sim q\ \vee \sim p)$ $\equiv$ $(p\ \wedge \sim q)\ \vee (p\ \wedge\sim p)$ $\equiv$ $(p\ \wedge \sim q)\$
2. $p\ \wedge \sim q$
3. $p\ \Rightarrow (p\wedge q)$$\equiv \sim p\ \vee (p \wedge \ q)$$\equiv$ $(\sim p\ \vee p)\ \wedge (\sim p \wedge \ q)$ $\equiv$ $(\sim p\ \wedge q)\$
4. $p\ \Rightarrow (p\vee q)$$\equiv \sim p\ \vee (p \vee \ q)$$\equiv$  $\sim p\ \vee p \vee \ q $$\equiv 1\vee \ q$$\equiv$  $1$
$\therefore$ Option D. is correct.