GATE2009 q26 - Revision history

Arjun Suresh at 22:32, 16 April 2015

2015-04-16T22:32:05Z

Arjun Suresh at 20:55, 15 September 2014

2014-09-15T20:55:24Z

Arjun Suresh at 11:46, 15 July 2014

2014-07-15T11:46:40Z

Arjun Suresh at 20:04, 14 July 2014

2014-07-14T20:04:39Z

Arjun Suresh at 20:03, 14 July 2014

2014-07-14T20:03:41Z

Arjun Suresh at 20:02, 14 July 2014

2014-07-14T20:02:48Z

Arjun Suresh: Created page with "Consider the following well-formed formulae:
I. ¬∀x(P(x)) II. ¬∃x(P(x)) III. ¬∃x(¬P(x)) IV. &exist..."

2014-07-14T20:00:28Z

Created page with "Consider the following well-formed formulae: I. ¬∀x(P(x)) II. ¬∃x(P(x)) III. ¬∃x(¬P(x)) IV. &exist..."

New page

Consider the following well-formed formulae:
 
I. ¬∀x(P(x))
 
II. ¬∃x(P(x))
 
III. ¬∃x(¬P(x))
 
IV. ∃x(¬P(x))
 
Which of the above are equivalent?
 
(A) I and III
 
(B) I and IV
 
(C) II and III
 
(D) II and IV

==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
A formula ∀x(P(x)) is equivalent to formula ¬∃x(¬P(x)) i.e. add ¬ inside and outside, and
convert ∀ to ∃.
 
So, ¬∀x(P(x)) is equivalent to ∃x(¬P(x)). So option (B) is correct.

{{Template:FBD}}

[[Category: GATE2009]]
[[Category: Graph Theory questions]]

← Older revision		Revision as of 22:32, 16 April 2015
Line 29:		Line 29:

	[[Category: GATE2009]]		[[Category: GATE2009]]
−	[[Category: ~~Logical Inference~~ questions from GATE]]	+	[[Category: Mathematical Logic questions from GATE]]

@@ Line 1: / Line 1: @@
 Consider the following well-formed formulae:
-		I. $&not;&forall;x(P(x))$
+		I. $\neg \forall x(P(x))$
-		II. $&not;&exist;x(P(x))$
+		II. $\neg \exists x(P(x))$
-		III. $&not;&exist;x(&not;P(x))$
+		III. $\neg \exists x(\neg P(x))$
-		IV. $&exist;x(&not;P(x))$
+		IV. $\exists x(\neg P(x))$
 		Which of the above are equivalent?

← Older revision		Revision as of 11:46, 15 July 2014
Line 29:		Line 29:

	[[Category: GATE2009]]		[[Category: GATE2009]]
−	[[Category: Logical Inference questions]]	+	[[Category: Logical Inference questions from GATE]]

← Older revision		Revision as of 20:04, 14 July 2014
Line 29:		Line 29:

	[[Category: GATE2009]]		[[Category: GATE2009]]
−	[[Category: ~~Graph Theory~~ questions]]	+	[[Category: Logical Inference questions]]

@@ Line 1: / Line 1: @@
 Consider the following well-formed formulae:
-		<br>
 		I. $&not;&forall;x(P(x))$
-		&nbsp;
 		II. $&not;&exist;x(P(x))$
-		&nbsp;
 		III. $&not;&exist;x(&not;P(x))$
-		&nbsp;
 		IV. $&exist;x(&not;P(x))$
-		<br>
 		Which of the above are equivalent?
@@ Line 21: / Line 21: @@
 ==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
 A formula $&forall;x(P(x))$ is equivalent to formula $&not;&exist;x(&not;P(x))$ i.e. add $&not;$ inside and outside, and
-		convert $&forall;$ to &exist;$.
+		convert $&forall;$ to $&exist;$.
-		<br>
 		So, $&not;&forall;x(P(x))$ is equivalent to $&exist;x(&not;P(x))$.

@@ Line 1: / Line 1: @@
 Consider the following well-formed formulae:
 		<br>
-		I. &not;&forall;x(P(x))
+		I. $&not;&forall;x(P(x))$
 		&nbsp;
-		II. &not;&exist;x(P(x))
+		II. $&not;&exist;x(P(x))$
 		&nbsp;
-		III. &not;&exist;x(&not;P(x))
+		III. $&not;&exist;x(&not;P(x))$
 		&nbsp;
-		IV. &exist;x(&not;P(x))
+		IV. $&exist;x(&not;P(x))$
 		<br>
 		Which of the above are equivalent?
-		<br>
-		<b>(A) </b>I and III
+(A) I and III
-		&nbsp;
-		<b>(B) </b>I and IV
+'''(B) I and IV'''
-		&nbsp;
-		<b>(C) </b>II and III
+(C) II and III
-		&nbsp;
-		<b>(D) </b>II and IV
+(D) II and IV
 ==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
-A formula &forall;x(P(x)) is equivalent to formula &not;&exist;x(&not;P(x)) i.e. add &not; inside and outside, and
+A formula $&forall;x(P(x))$ is equivalent to formula $&not;&exist;x(&not;P(x))$ i.e. add $&not;$ inside and outside, and
-		convert &forall; to &exist;.
+		convert $&forall;$ to &exist;$.
 		<br>
-		So, &not;&forall;x(P(x)) is equivalent to &exist;x(&not;P(x)). So option <b>(B)</b> is correct.
+		So, $&not;&forall;x(P(x))$ is equivalent to $&exist;x(&not;P(x))$.