Verified Solution • 2025–26 Session moderate

QJEEM23Ma230e: JEE Main 2023 Mathematics - Class 11 JEEM23Ma230e Solution: If p , q and r are three propositions, then which of the…

If p,q and r are three propositions, then which of the following combination of truth values of p,q and r makes the logical expression {(p∨q)∧((∼p)∨r)}→((∼q)∨r) false?

Multiple Choice Options

  • A p=F,q=T,r=F
  • B p=T,q=T,r=F
  • C p=T,q=F,r=T
  • D p=T,q=F,r=F

Step-by-Step Verified Solution

p\mathrm{p} q\mathrm{q} r\mathrm{r} (p∨q)∧((∼p)∨r)(p \vee q) \wedge((\sim p) \vee r) ∼q∨r\sim \mathrm{q} \vee \mathrm{r}
(1)(1) T\mathrm{T} F\mathrm{F} T\mathrm{T} T\mathrm{T} T\mathrm{T}
(2)(2) T\mathrm{T} T\mathrm{T} F\mathrm{F} F\mathrm{F} F\mathrm{F}
(3)(3) F\mathrm{F} T\mathrm{T} F\mathrm{F} T\mathrm{T} F\mathrm{F}
(4)(4) T\mathrm{T} F\mathrm{F} F\mathrm{F} F\mathrm{F} T\mathrm{T}

So, (p∨q)∧(∼q∨r)→(∼p∨r)(p \vee q) \wedge(\sim q \vee r) \rightarrow(\sim p \vee r) will be False.

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