Question

complete the following truth table. use t for true and f for false. in this table, p and q are statements. p q $q land p$ $q lor p$ t t $square$ $square$ t f $square$ $square$ f t $square$ $square$ f f $square$ $square$

Explanation:

Step1: Define conjunction rule

A conjunction $q \land p$ is true only if both $q$ and $p$ are true; else false.

Step2: Define disjunction rule

A disjunction $q \lor p$ is true if at least one of $q$ or $p$ is true; false only if both are false.

Step3: Evaluate row 1 (p=T, q=T)

$q \land p = T \land T = T$; $q \lor p = T \lor T = T$

Step4: Evaluate row 2 (p=T, q=F)

$q \land p = F \land T = F$; $q \lor p = F \lor T = T$

Step5: Evaluate row 3 (p=F, q=T)

$q \land p = T \land F = F$; $q \lor p = T \lor F = T$

Step6: Evaluate row 4 (p=F, q=F)

$q \land p = F \land F = F$; $q \lor p = F \lor F = F$

Answer:

$p$	$q$	$q \land p$	$q \lor p$
T	F	F	T
F	T	F	T
F	F	F	F