The maximum number of compound propositions, out of $p ∨ r ∨ s, p ∨ r ∨ ~ s, p ∨ ~ q ∨ s$ ,
$~ p ∨ ~ r ∨ s, ~ p ∨ ~ r ∨ ~ s, ~ p ∨ q ∨ ~ s,$
$q ∨ r ∨ ~ s, q ∨ ~ r ∨ ~ s, ~ p ∨ ~ q ∨ ~ s$
that can be made simultaneously true by an assignment of the truth values to $p, q, r$ and $s$ , is equal to

Question

The maximum number of compound propositions, out of

p ∨ r ∨ s, p ∨ r ∨ ~ s, p ∨ ~ q ∨ s

,

~ p ∨ ~ r ∨ s, ~ p ∨ ~ r ∨ ~ s, ~ p ∨ q ∨ ~ s,

q ∨ r ∨ ~ s, q ∨ ~ r ∨ ~ s, ~ p ∨ ~ q ∨ ~ s

that can be made simultaneously true by an assignment of the truth values to

p, q, r

and

s

, is equal to

Quantrex Academy · Accepted Answer

Correct answer: 0

If we take p q r s F F T F Put all the above truth value and check, p ∨ r ∨ s ⇒ True , p ∨ r ∨ ~ s ⇒ True p ∨ ~ q ∨ s ⇒ True ~ p ∨ ~ r ∨ s ⇒ True ~ p ∨ ~ r ∨ ~ s ⇒ True ~ p ∨ q ∨ ~ s ⇒ True q ∨ r ∨ ~ s ⇒ True q ∨ ~ r ∨ ~ s ⇒ True ~ p ∨ ~ q ∨ ~ s ⇒ True We can see the truth value of all the propositions will is true, so total 9

$p$	$q$	$r$	$s$
$F$	$F$	$T$	$F$

The maximum number of compound propositions, out of p ∨ r ∨ s, p ∨...

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