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  • Let <img alt="\mathrm{\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5CDelta%20%5Cin%5C%7B%5Cwedge%2C%20%5Cvee%2C%20%5C

Let \mathrm{\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}} be such that \mathrm{(p \wedge q) \Delta((p \vee q) \Rightarrow q)} is a tautology. Then \mathrm{\Delta} is equal to:

Option: 1

\wedge


Option: 2

\vee


Option: 3

\Rightarrow


Option: 4

\Leftrightarrow


Answers (1)

best_answer
\mathrm{ p} \mathrm{ q} \mathrm{p\wedge q} \mathrm{p\vee q} \mathrm{\left ( p\vee q \right )\Rightarrow q}
T T T T T
T F F T F
F T F T T
F F F F T

Looking at third ad fifth coloums, given statement will be a tautology only when \mathrm{ \Delta \: is\: \Rightarrow }

Hence the correct answer is option 3.

Posted by

Deependra Verma

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