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← JEE Main 2022 · 28 Jun · Shift 2
MathematicsInteger+4 / -1Question 30 of 90

JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 30

The maximum number of compound propositions, out of p∨r∨sp\vee r\vee s, p∨r∨∼sp\vee r\vee\sim s, p∨∼q∨sp\vee\sim q\vee s, ∼p∨∼r∨s\sim p\vee\sim r\vee s, ∼p∨∼r∨∼s\sim p\vee\sim r\vee\sim s, ∼p∨q∨∼s\sim p\vee q\vee\sim s, q∨r∨∼sq\vee r\vee\sim s, q∨∼r∨∼sq\vee\sim r\vee\sim s, ∼p∨∼q∨∼s\sim p\vee\sim q\vee\sim s that can be made simultaneously true by an assignment of the truth values to pp, qq, rr and ss, is equal to ______.

Answer and worked solution

Official answer: 9

One assignment works for all nine. p=F,q=F,r=T,s=Fp=F,q=F,r=T,s=F makes all nine true: the first two contain rr, the third ∼q\sim q, the four with ∼p\sim p are true, and the last two of the rest contain rr or ∼s\sim s.

Answer: 9

Topics:Mathematical reasoning
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