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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∨∼s,q∨r∨∼s,q∨∼∨∼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
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∨∼s,q∨r∨∼s,q∨∼∨∼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
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Solution
There are total 9 compound propositions, out of which 6 contain ∼s. So if we assign s as false, these 6 propositions will be true.
In remaining 3 compound propositions, two contain p and the third contains ∼r. So if we assign p and r as true and false respectively, these 3 propositions will also be true.
Hence maximum number of propositions that can be true are 9.
In remaining 3 compound propositions, two contain p and the third contains ∼r. So if we assign p and r as true and false respectively, these 3 propositions will also be true.
Hence maximum number of propositions that can be true are 9.
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