Question

1. $(p land

eg q) lor (
eg p land q)$

$p$	$t$	$t$	$f$	$f$
$q$	$t$	$f$	$t$	$f$

| $
eg p$ | $f$ | $f$ | $t$ | $t$ |
| $
eg q$ | $f$ | $t$ | $f$ | $t$ |
| $p land
eg q$ | $f$ | $t$ | $f$ | $f$ |
| $
eg p land q$ | $f$ | $f$ | $t$ | $f$ |
| $(p land
eg q) lor (
eg p land q)$ | $f$ | $t$ | $t$ | $f$ |

Explanation:

Step1: Verify $

eg p$ and $
eg q$
Given $p$ and $q$ truth values, $
eg p$ is opposite of $p$, $
eg q$ is opposite of $q$.

• Row1: $p=T,q=T \implies

eg p=F,
eg q=F$

• Row2: $p=T,q=F \implies

eg p=F,
eg q=T$

• Row3: $p=F,q=T \implies

eg p=T,
eg q=F$

• Row4: $p=F,q=F \implies

eg p=T,
eg q=T$

Step2: Calculate $p \land

eg q$
Conjunction is true only if both are true.

• Row1: $T \land F = F$
• Row2: $T \land T = T$
• Row3: $F \land F = F$
• Row4: $F \land T = F$

Step3: Calculate $

eg p \land q$
Conjunction is true only if both are true.

• Row1: $F \land T = F$
• Row2: $F \land F = F$
• Row3: $T \land T = T$
• Row4: $T \land F = F$

Step4: Calculate final disjunction

Disjunction is true if at least one is true.

• Row1: $F \lor F = F$
• Row2: $T \lor F = T$
• Row3: $F \lor T = T$
• Row4: $F \lor F = F$

Answer:

The completed truth table for $(p \land
eg q) \lor (
eg p \land q)$ has final column values (top to bottom): $\boldsymbol{F, T, T, F}$