Philosophy/PS1 - Revision history

Lensovet: all truth tables inserted...

2009-02-06T05:53:29Z

all truth tables inserted...

2009-02-06T05:35:37Z

10b

2009-02-06T05:26:10Z

2009-02-06T05:12:05Z

2009-02-06T04:50:42Z

2009-02-06T04:39:03Z

2009-02-06T04:26:04Z

2009-02-06T04:15:33Z

2009-02-06T04:05:21Z

up to 4

2009-02-06T03:53:45Z

@@ Line 99: / Line 99: @@
 .
 (a)
 . (a) Compare the values of the 2nd and 3rd rows; if they are equivalent, then # is commutative. Otherwise, it isn't.

@@ Line 106: / Line 106: @@
 .
 (a) No. Say p = "God exists", but there is actually no God. Many people believe God exists is true. Say p = "oceans are blue", which they are. Many people believe oceans are blue is true. Thus the truth value of the statement depends on more than just the truth-value of its single component.
-(b)
+(b) No. Say p = "the sun's gravitational field exerts an attractive force on all objects", q = "some frogs are green"; then the whole statement is false. However, say p remains the same and q = "the planets orbit around the sun"; then, the whole statement is true. Thus the whole statement can be both true and false if p & q are both true, and it is not truth-functional as the truth-values of p & q alone do not determine its truth value.
 (c) Yes; this is simply the "not" connective, whose output depends solely on the truth value of the input.

@@ Line 102: / Line 102: @@
 . (a) Compare the values of the 2nd and 3rd rows; if they are equivalent, then # is commutative. Otherwise, it isn't.
-(b) ??
+(b) Say P and Q are equivalent, i.e. both true. Then, for a connective to be anti-commutative, that means that P#Q is equivalent to -(Q#P). However, this is impossible as P#Q and Q#P are equivalent, so the negation of the latter cannot be equivalent to the former.
 .

← Older revision		Revision as of 05:12, 6 February 2009
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	9. (a) Compare the values of the 2nd and 3rd rows; if they are equivalent, then # is commutative. Otherwise, it isn't.		9. (a) Compare the values of the 2nd and 3rd rows; if they are equivalent, then # is commutative. Otherwise, it isn't.
		+	(b) ??
		+
		+	10.
		+	(a) No. Say p = "God exists", but there is actually no God. Many people believe God exists is true. Say p = "oceans are blue", which they are. Many people believe oceans are blue is true. Thus the truth value of the statement depends on more than just the truth-value of its single component.
		+	(b)
		+	(c) Yes; this is simply the "not" connective, whose output depends solely on the truth value of the input.

← Older revision		Revision as of 04:50, 6 February 2009
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	\|F \|\| F \|\| F \|\| F \|\| F \|\| F		\|F \|\| F \|\| F \|\| F \|\| F \|\| F
	\|}		\|}
		+
		+	6.
		+	(a)
		+
		+	9. (a) Compare the values of the 2nd and 3rd rows; if they are equivalent, then # is commutative. Otherwise, it isn't.

@@ Line 76: / Line 76: @@
 |-
 | F || F || F || F || T || F || F || T
 |}

@@ Line 21: / Line 21: @@
 .
 {|
 ! p || q || r || p.-r || p.q || p.q ⊃ r || p.-r ∨ (p.q ⊃ r)
@@ Line 39: / Line 40: @@
 |-
 |F || F || F || F || F || T || T
 |}

← Older revision		Revision as of 04:15, 6 February 2009
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	(e) (-French object to pact . -Belgians object to pact) . Italian forces withdraw from Spain . attacks on British ships cease ⊃ Italo-British pact will take effect		(e) (-French object to pact . -Belgians object to pact) . Italian forces withdraw from Spain . attacks on British ships cease ⊃ Italo-British pact will take effect
	(f) (-Mail-order campaign breaks Dripsweet monopoly . -mail-order campaign restores competition) ⊃ Jones will mortgage his home ∨ (Jones will sell his car . Jones will sell his boat)		(f) (-Mail-order campaign breaks Dripsweet monopoly . -mail-order campaign restores competition) ⊃ Jones will mortgage his home ∨ (Jones will sell his car . Jones will sell his boat)
		+
		+	5.
		+	{\|
		+	! p \|\| q \|\| r \|\| p.-r \|\| p.q \|\| p.q ⊃ r \|\| p.-r ∨ (p.q ⊃ r)
		+	\|-
		+	\|T \|\| T \|\| T \|\| F \|\| T \|\| T \|\| T
		+	\|-
		+	\|T \|\| T \|\| F \|\| T \|\| T \|\| F \|\| T
		+	\|-
		+	\|T \|\| F \|\| T \|\| F \|\| F \|\| T \|\| T
		+	\|-
		+	\|T \|\| F \|\| F \|\| T \|\| F \|\| T \|\| T
		+	\|-
		+	\|F \|\| T \|\| T \|\| F \|\| F \|\| T \|\| T
		+	\|-
		+	\|F \|\| T \|\| F \|\| F \|\| F \|\| T \|\| T
		+	\|-
		+	\|F \|\| F \|\| T \|\| F \|\| F \|\| T \|\| T
		+	\|-
		+	\|F \|\| F \|\| F \|\| F \|\| F \|\| T \|\| T
		+	\|}

@@ Line 15: / Line 15: @@
 (a) George will cut down a tree . (George will marry Martha ∨ George will die a bachelor)
 (b) (Abe will not become mayor . city will not prosper) ∨ (Abe will become mayor . Ava will become head of chamber of commerce)
-(c) (Steve escapes the country ∨ Steve befriends Sally)
+(c) (Steve escapes the country ∨ Steve befriends Sally) ⊃ Steve will be safe

← Older revision		Revision as of 03:53, 6 February 2009
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	3. Neither the President is happy nor is Congress placated; The President is not happy or Congress is placated.		3. Neither the President is happy nor is Congress placated; The President is not happy or Congress is placated.

−	4. George will cut down a tree . (George will marry Martha ∨ George will die a bachelor)	+	4.
		+	(a) George will cut down a tree . (George will marry Martha ∨ George will die a bachelor)
		+	(b) (Abe will not become mayor . city will not prosper) ∨ (Abe will become mayor . Ava will become head of chamber of commerce)
		+	(c) (Steve escapes the country ∨ Steve befriends Sally)