JEE Main 2023 · 29 January · Morning Shift · Mathematics · Mathematical Reasoning
If p, q and r are three propositions, then which of the following...
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 ?
Options
Ap=T,q=F,r=T
Bp=T,q=T,r=F
Cp=F,q=T,r=F
Dp=T,q=F,r=F
Correct answer
C. p=F,q=T,r=F
Step-by-step solution
Given,
(p∨q)∧((p)∨r)→((q)∨r)
Now solving the above expression using truth table from given options we get,
p
q
r
\left(p ∨ q\right)</td><td>(p∨r)
A ≡ \left(p ∨ q\right)∧(p∨r)
B≡q∨r
A \to B</td></tr><tr><td>(A)</td><td>T</td><td>F</td><td>T</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">T</td></tr><tr><td>(B)</td><td>T</td><td>T</td><td>F</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">F</td><tdstyle="text−align:center;">F</td><tdstyle="text−align:center;">F</td><tdstyle="text−align:center;">T</td></tr><tr><td>(C)</td><td>F</td><td>T</td><td>F</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">F</td><tdstyle="text−align:center;">F</td></tr><tr><td>(D)</td><td>T</td><td>F</td><td>F</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">F</td><tdstyle="text−align:center;">F</td><tdstyle="text−align:center;">T</td><tdstyle="text−align:center;">T</td></tr></tbody></table><p>So,onlyOptionC will be false.
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