Tag: logical equivalence

Questions Related to logical equivalence

Which one of the following statements is a tautology?

logical equivalence mathematical logic discrete mathematics business maths maths

  1. $\left( p\vee q \right) \rightarrow q$

  2. $p\vee (p\rightarrow q)$

  3. $ p\vee (q\rightarrow p)$

  4. $p\rightarrow (p\rightarrow q)$

Show answer
Correct Option: B
Explanation:
$ p$  $q$  $p\to q$  $q\to p$ $pvq$  $p\to (p\to q)$  $(pvq)\to q$  $pv(p\to q)$   $pv(q\to q$
 T  T  T  T  T  T  T  T  T
 T  F  F  T  T  F  F  T  T
 F  T  T  F  T  T  T  T  F
 F  F  T  T  F  T  T  T  T

$\left( p\vee q \right) \rightarrow q$

If $p$ and $q$ are two statement, then $(p  \wedge \sim q) \wedge   (\sim p  \wedge   q)$ is

logical equivalence mathematical logic discrete mathematics business maths maths

  1. a fallacy

  2. a tautology

  3. neither tautology nor a fallacy

  4. none of these

Show answer
Correct Option: A
Explanation:
$p$         $q$          $p \land \sim q$       $q \land \sim p $          $(p \land \sim q ) \land(q \land \sim p )$
T T     F       F          F
T F     T       F          F
F T      F       T          F
F F     F       F          F


$\therefore\ (p \land \sim q ) \land(q \land \sim p )$ is a fallacy