Verified Solution • 2025–26 Session moderate

QJEEM22Madcfe: JEE Main 2022 Mathematics - Class 11 JEEM22Madcfe Solution: The maximum number of compound propositions, out of p ∨ r ∨ s,…

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 __________.

Step-by-Step Verified Solution

There are total 9 compound propositions, out of which 6 contain ∼s\sim s . So if we assign ss as false, these 6 propositions will be true.

In remaining 3 compound propositions, two contain pp and the third contains ∼r\sim r . So if we assign pp and rr 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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