Problem in understanding the meaning of a quantified conditional statement based on the position of the...
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Let the universe of discourse be the set of all human beings. $M(x)$ is an open statement which stands for "x is a man" and $B(x)$ stands for "x has black hair".
I have problem understanding how the statement
$neg(forall x)(M(x) rightarrow B(x))$ is different in meaning from $(forall x)neg(M(x)rightarrow B(x))$ in meaning.
Is my understanding correct if I say statement 1 means not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
predicate-logic quantifiers
asked Nov 25 at 0:39
Mainul Islam
1034
closed as off-topic by Adrian Keister, Scientifica, user10354138, Did, José Carlos Santos Nov 25 at 11:52
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Adrian Keister, Scientifica, user10354138, Did, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
0
down vote
favorite
Let the universe of discourse be the set of all human beings. $M(x)$ is an open statement which stands for "x is a man" and $B(x)$ stands for "x has black hair".
I have problem understanding how the statement
$neg(forall x)(M(x) rightarrow B(x))$ is different in meaning from $(forall x)neg(M(x)rightarrow B(x))$ in meaning.
Is my understanding correct if I say statement 1 means not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
predicate-logic quantifiers
asked Nov 25 at 0:39
Mainul Islam
1034
closed as off-topic by Adrian Keister, Scientifica, user10354138, Did, José Carlos Santos Nov 25 at 11:52
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Adrian Keister, Scientifica, user10354138, Did, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
1
Have you tried rewriting them in English? The second starts "For all men ..." and I would begin a sentence for the first one with "There is a man ..." to deal with the "not for all".
– Ethan Bolker
Nov 25 at 0:50
The edit changes what I suggest the sentences say but not the recommendation to say it in English.
– Ethan Bolker
Nov 25 at 1:26
Yes I have and would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN has black hair?
– Mainul Islam
Nov 25 at 1:47
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let the universe of discourse be the set of all human beings. $M(x)$ is an open statement which stands for "x is a man" and $B(x)$ stands for "x has black hair".
I have problem understanding how the statement
$neg(forall x)(M(x) rightarrow B(x))$ is different in meaning from $(forall x)neg(M(x)rightarrow B(x))$ in meaning.
Is my understanding correct if I say statement 1 means not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
predicate-logic quantifiers
asked Nov 25 at 0:39
Mainul Islam
1034
Let the universe of discourse be the set of all human beings. $M(x)$ is an open statement which stands for "x is a man" and $B(x)$ stands for "x has black hair".
I have problem understanding how the statement
$neg(forall x)(M(x) rightarrow B(x))$ is different in meaning from $(forall x)neg(M(x)rightarrow B(x))$ in meaning.
Is my understanding correct if I say statement 1 means not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
predicate-logic quantifiers
predicate-logic quantifiers
asked Nov 25 at 0:39
Mainul Islam
1034
asked Nov 25 at 0:39
Mainul Islam
1034
edited Nov 29 at 8:16
asked Nov 25 at 0:39
Mainul Islam
1034
asked Nov 25 at 0:39
Mainul Islam
1034
asked Nov 25 at 0:39
Mainul Islam
1034
1034
closed as off-topic by Adrian Keister, Scientifica, user10354138, Did, José Carlos Santos Nov 25 at 11:52
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Adrian Keister, Scientifica, user10354138, Did, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Adrian Keister, Scientifica, user10354138, Did, José Carlos Santos Nov 25 at 11:52
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Adrian Keister, Scientifica, user10354138, Did, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
1
Have you tried rewriting them in English? The second starts "For all men ..." and I would begin a sentence for the first one with "There is a man ..." to deal with the "not for all".
– Ethan Bolker
Nov 25 at 0:50
The edit changes what I suggest the sentences say but not the recommendation to say it in English.
– Ethan Bolker
Nov 25 at 1:26
Yes I have and would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN has black hair?
– Mainul Islam
Nov 25 at 1:47
add a comment |
1
Have you tried rewriting them in English? The second starts "For all men ..." and I would begin a sentence for the first one with "There is a man ..." to deal with the "not for all".
– Ethan Bolker
Nov 25 at 0:50
The edit changes what I suggest the sentences say but not the recommendation to say it in English.
– Ethan Bolker
Nov 25 at 1:26
Yes I have and would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN has black hair?
– Mainul Islam
Nov 25 at 1:47
1
1
Have you tried rewriting them in English? The second starts "For all men ..." and I would begin a sentence for the first one with "There is a man ..." to deal with the "not for all".
– Ethan Bolker
Nov 25 at 0:50
Have you tried rewriting them in English? The second starts "For all men ..." and I would begin a sentence for the first one with "There is a man ..." to deal with the "not for all".
– Ethan Bolker
Nov 25 at 0:50
The edit changes what I suggest the sentences say but not the recommendation to say it in English.
– Ethan Bolker
Nov 25 at 1:26
The edit changes what I suggest the sentences say but not the recommendation to say it in English.
– Ethan Bolker
Nov 25 at 1:26
Yes I have and would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN has black hair?
– Mainul Islam
Nov 25 at 1:47
Yes I have and would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN has black hair?
– Mainul Islam
Nov 25 at 1:47
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
The first statement means that it is not true that every man has black hair
The second statement is equivalent to $forall x (M(x) land neg H(x))$ and thus means that everything in the domain is a man and does not have black hair
I asume you can see the difference now ...
answered Nov 25 at 1:22
Bram28
58.7k44185
Would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
– Mainul Islam
Nov 25 at 1:46
Statement two is actually a good but stronger than that: nothing has black hair under statement two
– Bram28
Nov 25 at 1:51
I mean no argument. Only trying to understand it fully. But isn't it the case that statement 2 is logically equivalent to $(forall x)(neg M(x) vee B(x))$?
– Mainul Islam
Nov 25 at 2:18
1
@mainulislam No. $forall x neg (M(x) rightarrow H(x))$ is equivalent to $forall x neg (neg M(x) lor H(x))$ and thus to $forall x (M(x) land neg H(x))$
– Bram28
Nov 25 at 12:32
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
The first statement means that it is not true that every man has black hair
The second statement is equivalent to $forall x (M(x) land neg H(x))$ and thus means that everything in the domain is a man and does not have black hair
I asume you can see the difference now ...
answered Nov 25 at 1:22
Bram28
58.7k44185
Would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
– Mainul Islam
Nov 25 at 1:46
Statement two is actually a good but stronger than that: nothing has black hair under statement two
– Bram28
Nov 25 at 1:51
I mean no argument. Only trying to understand it fully. But isn't it the case that statement 2 is logically equivalent to $(forall x)(neg M(x) vee B(x))$?
– Mainul Islam
Nov 25 at 2:18
1
@mainulislam No. $forall x neg (M(x) rightarrow H(x))$ is equivalent to $forall x neg (neg M(x) lor H(x))$ and thus to $forall x (M(x) land neg H(x))$
– Bram28
Nov 25 at 12:32
add a comment |
up vote
0
down vote
accepted
The first statement means that it is not true that every man has black hair
The second statement is equivalent to $forall x (M(x) land neg H(x))$ and thus means that everything in the domain is a man and does not have black hair
I asume you can see the difference now ...
answered Nov 25 at 1:22
Bram28
58.7k44185
Would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
– Mainul Islam
Nov 25 at 1:46
Statement two is actually a good but stronger than that: nothing has black hair under statement two
– Bram28
Nov 25 at 1:51
I mean no argument. Only trying to understand it fully. But isn't it the case that statement 2 is logically equivalent to $(forall x)(neg M(x) vee B(x))$?
– Mainul Islam
Nov 25 at 2:18
1
@mainulislam No. $forall x neg (M(x) rightarrow H(x))$ is equivalent to $forall x neg (neg M(x) lor H(x))$ and thus to $forall x (M(x) land neg H(x))$
– Bram28
Nov 25 at 12:32
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
The first statement means that it is not true that every man has black hair
The second statement is equivalent to $forall x (M(x) land neg H(x))$ and thus means that everything in the domain is a man and does not have black hair
I asume you can see the difference now ...
answered Nov 25 at 1:22
Bram28
58.7k44185
The first statement means that it is not true that every man has black hair
The second statement is equivalent to $forall x (M(x) land neg H(x))$ and thus means that everything in the domain is a man and does not have black hair
I asume you can see the difference now ...
answered Nov 25 at 1:22
Bram28
58.7k44185
answered Nov 25 at 1:22
Bram28
58.7k44185
answered Nov 25 at 1:22
Bram28
58.7k44185
answered Nov 25 at 1:22
Bram28
58.7k44185
58.7k44185
Would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
– Mainul Islam
Nov 25 at 1:46
Statement two is actually a good but stronger than that: nothing has black hair under statement two
– Bram28
Nov 25 at 1:51
I mean no argument. Only trying to understand it fully. But isn't it the case that statement 2 is logically equivalent to $(forall x)(neg M(x) vee B(x))$?
– Mainul Islam
Nov 25 at 2:18
1
@mainulislam No. $forall x neg (M(x) rightarrow H(x))$ is equivalent to $forall x neg (neg M(x) lor H(x))$ and thus to $forall x (M(x) land neg H(x))$
– Bram28
Nov 25 at 12:32
add a comment |
Would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
– Mainul Islam
Nov 25 at 1:46
Statement two is actually a good but stronger than that: nothing has black hair under statement two
– Bram28
Nov 25 at 1:51
I mean no argument. Only trying to understand it fully. But isn't it the case that statement 2 is logically equivalent to $(forall x)(neg M(x) vee B(x))$?
– Mainul Islam
Nov 25 at 2:18
1
@mainulislam No. $forall x neg (M(x) rightarrow H(x))$ is equivalent to $forall x neg (neg M(x) lor H(x))$ and thus to $forall x (M(x) land neg H(x))$
– Bram28
Nov 25 at 12:32
Would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
– Mainul Islam
Nov 25 at 1:46
Would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
– Mainul Islam
Nov 25 at 1:46
Statement two is actually a good but stronger than that: nothing has black hair under statement two
– Bram28
Nov 25 at 1:51
Statement two is actually a good but stronger than that: nothing has black hair under statement two
– Bram28
Nov 25 at 1:51
I mean no argument. Only trying to understand it fully. But isn't it the case that statement 2 is logically equivalent to $(forall x)(neg M(x) vee B(x))$?
– Mainul Islam
Nov 25 at 2:18
I mean no argument. Only trying to understand it fully. But isn't it the case that statement 2 is logically equivalent to $(forall x)(neg M(x) vee B(x))$?
– Mainul Islam
Nov 25 at 2:18
1
1
@mainulislam No. $forall x neg (M(x) rightarrow H(x))$ is equivalent to $forall x neg (neg M(x) lor H(x))$ and thus to $forall x (M(x) land neg H(x))$
– Bram28
Nov 25 at 12:32
@mainulislam No. $forall x neg (M(x) rightarrow H(x))$ is equivalent to $forall x neg (neg M(x) lor H(x))$ and thus to $forall x (M(x) land neg H(x))$
– Bram28
Nov 25 at 12:32
add a comment |
1
Have you tried rewriting them in English? The second starts "For all men ..." and I would begin a sentence for the first one with "There is a man ..." to deal with the "not for all".
– Ethan Bolker
Nov 25 at 0:50
The edit changes what I suggest the sentences say but not the recommendation to say it in English.
– Ethan Bolker
Nov 25 at 1:26
Yes I have and would I be right in saying statement 1 means: not every man has black hair and statement 2 means: NO MAN has black hair?
– Mainul Islam
Nov 25 at 1:47