Which of the following Boolean expression s is not a tautology?

Option 1 -

$(\sim p \Rightarrow q) \lor (\sim q \Rightarrow p)$

Option 2 -

$(q \Rightarrow p) \lor (\sim q \Rightarrow p)$

Option 3 -

$(p \Rightarrow \sim q) \lor (\sim q \Rightarrow p)$

Option 4 -

$(p \Rightarrow q) \lor (\sim q \Rightarrow p)$

1 View | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 1

Detailed Solution:

Option (A)

p	q		q	p -> q	q -> p	q ->p	( p -> q) ( q -> p)
T	T	F	F	T	T	T	T
T	F	F	T	T	T	T	T
F	T	T	F	T	T	F	T
F	F	T	T	F	F	T	F

Option (B)

p	q		q	p -> q	q -> p	q -> p	( p -> q) ( q -> p)
T	T	F	F	T	T	T	T
T	F	F	T	T	T	T	T
F	T	T	F	T	T	F	T
F	F	T	T	F	F	T	T

Option (C)

p	q		q	p -> q	q -> p	q -> p	(p -> q) ( q -> p)
T	T	F	F	F	T	T	T
T	F	F	T	T	T	T	T
F	T	T	F	T	T	F	T
F	F	T	T	T	F	T	T

Option (D)

p	q		q	p ->q	q -> p	p -> q	(p ->q) ( q -> p)
T	T	F	F	T	T	T	T

T	F	F	T	T	T	F	T
F	T	T	F	T	T	T	T
F	F	T	T	F	F	T	T

Option (A)<table border="1" cellspacing="0" cellpadding="0"><tbody><tr><td valign="top" width="37">p</td><td valign="top" width="33">q</td><td valign="top" width="44"></td><td valign="top" width="39">q</td><td valign="top" width="56">p -> q</td><td valign="top" width="56">q -> p</td><td valign="top" width="56">q ->p</td><td valign="top" width="100">( p -> q) ( q -> p)</td></tr><tr><td valign="top" width="37">T</td><td valign="top" width="33">T</td><td valign="top" width="44">F</td><td valign="top" width="39">F</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="100">T</td></tr><tr><td valign="top" width="37">T</td><td valign="top" width="33">F</td><td valign="top" width="44">F</td><td valign="top" width="39">T</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="100">T</td></tr><tr><td valign="top" width="37">F</td><td valign="top" width="33">T</td><td valign="top" width="44">T</td><td valign="top" width="39">F</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="56">F</td><td valign="top" width="100">T</td></tr><tr><td valign="top" width="37">F</td><td valign="top" width="33">F</td><td valign="top" width="44">T</td><td valign="top" width="39">T</td><td valign="top" width="56">F</td><td valign="top" width="56">F</td><td valign="top" width="56">T</td><td valign="top" width="100">F</td></tr></tbody></table>              Option (B)<table border="1" cellspacing="0" cellpadding="0"><tbody><tr><td valign="top" width="37">p</td><td valign="top" width="33">q</td><td valign="top" width="44"></td><td valign="top" width="39">q</td><td valign="top" width="56">p -> q</td><td valign="top" width="56">q -> p</td><td valign="top" width="56">q -> p</td><td valign="top" width="100">( p -> q) ( q -> p)</td></tr><tr><td valign="top" width="37">T</td><td valign="top" width="33">T</td><td valign="top" width="44">F</td><td valign="top" width="39">F</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="100">T</td></tr><tr><td valign="top" width="37">T</td><td valign="top" width="33">F</td><td valign="top" width="44">F</td><td valign="top" width="39">T</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="100">T</td></tr><tr><td valign="top" width="37">F</td><td valign="top" width="33">T</td><td valign="top" width="44">T</td><td valign="top" width="39">F</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="56">F</td><td valign="top" width="100">T</td></tr><tr><td valign="top" width="37">F</td><td valign="top" width="33">F</td><td valign="top" width="44">T</td><td valign="top" width="39">T</td><td valign="top" width="56">F</td><td valign="top" width="56">F</td><td valign="top" width="56">T</td><td valign="top" width="100">T</td></tr></tbody></table>              Option (C)<table border="1" cellspacing="0" cellpadding="0"><tbody><tr><td valign="top" width="37">p</td><td valign="top" width="33">q</td><td valign="top" width="44"></td><td valign="top" width="39">q</td><td valign="top" width="56">p -> q</td><td valign="top" width="56">q -> p</td><td valign="top" width="56">q -> p</td><td valign="top" width="100">(p -> q) ( q -> p)</td></tr><tr><td valign="top" width="37">T</td><td valign="top" width="33">T</td><td valign="top" width="44">F</td><td valign="top" width="39">F</td><td valign="top" width="56">F</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="100">T</td></tr><tr><td valign="top" width="37">T</td><td valign="top" width="33">F</td><td valign="top" width="44">F</td><td valign="top" width="39">T</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="100">T</td></tr><tr><td valign="top" width="37">F</td><td valign="top" width="33">T</td><td valign="top" width="44">T</td><td valign="top" width="39">F</td><td valign="top" width="56">T</td><td valign="top" width="56">T</td><td valign="top" width="56">F</td><td valign="top" width="100">T</td></tr><tr><td valign="top" width="37">F</td><td valign="top" width="33">F</td><td valign="top" width="44">T</td><td valign="top" width="39">T</td><td valign="top" width="56">T</td><td valign="top" width="56">F</td><td valign="top" width="56">T</td><td valign="top" width="100">T</td></tr></tbody></table>              Option (D)<table border="1" cellspacing="0" cellpadding="0"><tbody><tr><td valign="top" width="37">p</td><td valign="top" width="33">q</td><td valign="top" width="43"></td><td valign="top" width="39">q</td><td valign="top" width="59">p ->q</td><td valign="top" width="55">q -> p</td><td valign="top" width="55">p -> q</td><td valign="top" width="103">(p ->q) ( q -> p)</td></tr><tr><td valign="top" width="37">T</td><td valign="top" width="33">T</td><td valign="top" width="43">F</td><td valign="top" width="39">F</td><td valign="top" width="59">T</td><td valign="top" width="55">T</td><td valign="top" width="55">T</td><td valign="top" width="103">T</td></tr></tbody></table><table border="1" cellspacing="0" cellpadding="0"><tbody><tr><td valign="top" width="39">T</td><td valign="top" width="34">F</td><td valign="top" width="38">F</td><td valign="top" width="38">T</td><td valign="top" width="57">T</td><td valign="top" width="57">T</td><td valign="top" width="57">F</td><td valign="top" width="105">T</td></tr><tr><td valign="top" width="39">F</td><td valign="top" width="34">T</td><td valign="top" width="38">T</td><td valign="top" width="38">F</td><td valign="top" width="57">T</td><td valign="top" width="57">T</td><td valign="top" width="57">T</td><td valign="top" width="105">T</td></tr><tr><td valign="top" width="39">F</td><td valign="top" width="34">F</td><td valign="top" width="38">T</td><td valign="top" width="38">T</td><td valign="top" width="57">F</td><td valign="top" width="57">F</td><td valign="top" width="57">T</td><td valign="top" width="105">T</td></tr></tbody></table>

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