As i got the contrapositive of this statement, how does e) necessarily follows from this? [closed]
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An electronic circuit contains three light bulbs, X, Y and Z, which are each either on or off at
any particular time. It is known that if bulb X is off or bulb Y is on, then bulb Z is on.
Which one of these statements necessarily follows from this?
A. If bulb Z is on, then bulb X is off or bulb Y is on.
B. If bulb Z is on, then bulb X is on and bulb Y is off.
C. If bulb Z is on, then bulb X is on or bulb Y is on.
D. If bulb Z is off, then bulb X is off and bulb Y is off.
E. If bulb Z is off, then bulb X is on or bulb Y is off.
F. If bulb Z is off, then bulb X is on and bulb Y is on.
The contrapositive of the given statement is If bulb Z is off, then bulb X is on and bulb Y is off. However, apparently, there is no such choice in the given choices.
propositional-calculus
asked Dec 28 '18 at 14:28
KevinKevin
143
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closed as off-topic by José Carlos Santos, Holo, metamorphy, Abcd, user91500 Dec 29 '18 at 10:24
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, Holo, metamorphy, Abcd, user91500
If this question can be reworded to fit the rules in the help center, please edit the question.
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show 3 more comments
$begingroup$
An electronic circuit contains three light bulbs, X, Y and Z, which are each either on or off at
any particular time. It is known that if bulb X is off or bulb Y is on, then bulb Z is on.
Which one of these statements necessarily follows from this?
A. If bulb Z is on, then bulb X is off or bulb Y is on.
B. If bulb Z is on, then bulb X is on and bulb Y is off.
C. If bulb Z is on, then bulb X is on or bulb Y is on.
D. If bulb Z is off, then bulb X is off and bulb Y is off.
E. If bulb Z is off, then bulb X is on or bulb Y is off.
F. If bulb Z is off, then bulb X is on and bulb Y is on.
The contrapositive of the given statement is If bulb Z is off, then bulb X is on and bulb Y is off. However, apparently, there is no such choice in the given choices.
propositional-calculus
asked Dec 28 '18 at 14:28
KevinKevin
143
$endgroup$
closed as off-topic by José Carlos Santos, Holo, metamorphy, Abcd, user91500 Dec 29 '18 at 10:24
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, Holo, metamorphy, Abcd, user91500
If this question can be reworded to fit the rules in the help center, please edit the question.
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Did you try to put this into a logical expression?
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– Bram28
Dec 28 '18 at 14:35
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actly the answer is e,but i dont know why
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– Kevin
Dec 28 '18 at 14:38
1
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@Kevin You correctly found the the contrapositive ....now think a little about what that says ... and you'll see how e) logically follows from that. That is, answer e) is not equivalent to the original statement, but it does logically follow from it
$endgroup$
– Bram28
Dec 28 '18 at 14:46
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@Bram28 im sorry, could u please be more detail oriented on how does it follow from it
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– Kevin
Dec 28 '18 at 14:46
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@Kevin remember the logical "or" is inclusive. So, if I tell you that snow is white and grass is green, does it follow (in logic) that snow is white or grass is green?
$endgroup$
– Bram28
Dec 28 '18 at 14:46
|
show 3 more comments
$begingroup$
An electronic circuit contains three light bulbs, X, Y and Z, which are each either on or off at
any particular time. It is known that if bulb X is off or bulb Y is on, then bulb Z is on.
Which one of these statements necessarily follows from this?
A. If bulb Z is on, then bulb X is off or bulb Y is on.
B. If bulb Z is on, then bulb X is on and bulb Y is off.
C. If bulb Z is on, then bulb X is on or bulb Y is on.
D. If bulb Z is off, then bulb X is off and bulb Y is off.
E. If bulb Z is off, then bulb X is on or bulb Y is off.
F. If bulb Z is off, then bulb X is on and bulb Y is on.
The contrapositive of the given statement is If bulb Z is off, then bulb X is on and bulb Y is off. However, apparently, there is no such choice in the given choices.
propositional-calculus
asked Dec 28 '18 at 14:28
KevinKevin
143
$endgroup$
An electronic circuit contains three light bulbs, X, Y and Z, which are each either on or off at
any particular time. It is known that if bulb X is off or bulb Y is on, then bulb Z is on.
Which one of these statements necessarily follows from this?
A. If bulb Z is on, then bulb X is off or bulb Y is on.
B. If bulb Z is on, then bulb X is on and bulb Y is off.
C. If bulb Z is on, then bulb X is on or bulb Y is on.
D. If bulb Z is off, then bulb X is off and bulb Y is off.
E. If bulb Z is off, then bulb X is on or bulb Y is off.
F. If bulb Z is off, then bulb X is on and bulb Y is on.
The contrapositive of the given statement is If bulb Z is off, then bulb X is on and bulb Y is off. However, apparently, there is no such choice in the given choices.
propositional-calculus
propositional-calculus
asked Dec 28 '18 at 14:28
KevinKevin
143
asked Dec 28 '18 at 14:28
KevinKevin
143
edited Jan 2 at 13:39
Kevin
asked Dec 28 '18 at 14:28
KevinKevin
143
asked Dec 28 '18 at 14:28
KevinKevin
143
asked Dec 28 '18 at 14:28
KevinKevin
143
143
closed as off-topic by José Carlos Santos, Holo, metamorphy, Abcd, user91500 Dec 29 '18 at 10:24
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, Holo, metamorphy, Abcd, user91500
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by José Carlos Santos, Holo, metamorphy, Abcd, user91500 Dec 29 '18 at 10:24
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, Holo, metamorphy, Abcd, user91500
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Did you try to put this into a logical expression?
$endgroup$
– Bram28
Dec 28 '18 at 14:35
$begingroup$
actly the answer is e,but i dont know why
$endgroup$
– Kevin
Dec 28 '18 at 14:38
1
$begingroup$
@Kevin You correctly found the the contrapositive ....now think a little about what that says ... and you'll see how e) logically follows from that. That is, answer e) is not equivalent to the original statement, but it does logically follow from it
$endgroup$
– Bram28
Dec 28 '18 at 14:46
$begingroup$
@Bram28 im sorry, could u please be more detail oriented on how does it follow from it
$endgroup$
– Kevin
Dec 28 '18 at 14:46
$begingroup$
@Kevin remember the logical "or" is inclusive. So, if I tell you that snow is white and grass is green, does it follow (in logic) that snow is white or grass is green?
$endgroup$
– Bram28
Dec 28 '18 at 14:46
|
show 3 more comments
$begingroup$
Did you try to put this into a logical expression?
$endgroup$
– Bram28
Dec 28 '18 at 14:35
$begingroup$
actly the answer is e,but i dont know why
$endgroup$
– Kevin
Dec 28 '18 at 14:38
1
$begingroup$
@Kevin You correctly found the the contrapositive ....now think a little about what that says ... and you'll see how e) logically follows from that. That is, answer e) is not equivalent to the original statement, but it does logically follow from it
$endgroup$
– Bram28
Dec 28 '18 at 14:46
$begingroup$
@Bram28 im sorry, could u please be more detail oriented on how does it follow from it
$endgroup$
– Kevin
Dec 28 '18 at 14:46
$begingroup$
@Kevin remember the logical "or" is inclusive. So, if I tell you that snow is white and grass is green, does it follow (in logic) that snow is white or grass is green?
$endgroup$
– Bram28
Dec 28 '18 at 14:46
$begingroup$
Did you try to put this into a logical expression?
$endgroup$
– Bram28
Dec 28 '18 at 14:35
$begingroup$
Did you try to put this into a logical expression?
$endgroup$
– Bram28
Dec 28 '18 at 14:35
$begingroup$
actly the answer is e,but i dont know why
$endgroup$
– Kevin
Dec 28 '18 at 14:38
$begingroup$
actly the answer is e,but i dont know why
$endgroup$
– Kevin
Dec 28 '18 at 14:38
1
1
$begingroup$
@Kevin You correctly found the the contrapositive ....now think a little about what that says ... and you'll see how e) logically follows from that. That is, answer e) is not equivalent to the original statement, but it does logically follow from it
$endgroup$
– Bram28
Dec 28 '18 at 14:46
$begingroup$
@Kevin You correctly found the the contrapositive ....now think a little about what that says ... and you'll see how e) logically follows from that. That is, answer e) is not equivalent to the original statement, but it does logically follow from it
$endgroup$
– Bram28
Dec 28 '18 at 14:46
$begingroup$
@Bram28 im sorry, could u please be more detail oriented on how does it follow from it
$endgroup$
– Kevin
Dec 28 '18 at 14:46
$begingroup$
@Bram28 im sorry, could u please be more detail oriented on how does it follow from it
$endgroup$
– Kevin
Dec 28 '18 at 14:46
$begingroup$
@Kevin remember the logical "or" is inclusive. So, if I tell you that snow is white and grass is green, does it follow (in logic) that snow is white or grass is green?
$endgroup$
– Bram28
Dec 28 '18 at 14:46
$begingroup$
@Kevin remember the logical "or" is inclusive. So, if I tell you that snow is white and grass is green, does it follow (in logic) that snow is white or grass is green?
$endgroup$
– Bram28
Dec 28 '18 at 14:46
|
show 3 more comments
1 Answer
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From the comments, I gather you correctly found the contrapositive (you should really add that to your post ... in general, you should always add your work to your post). So, that is:
If Z is off, then X is on and Y is off
Now, this is almost the same as answer e) ... except in e) you have an 'or' rather than an 'and'
But, remember that in logic the 'or' is inclusive. So, if it is true that 'P and Q', then it follows that 'P or Q'.
Likewise, if Z is off, we know X is on and Y is off. But then it is also true that X is on or Y is off. So, if Z is off, then X is on or Y is off
So, the answer is e). e) is not logically equivalent to the original statement but, as we saw, it does logically follow from it, and that is what the question asked.
answered Dec 28 '18 at 14:53
Bram28Bram28
63.1k44793
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
From the comments, I gather you correctly found the contrapositive (you should really add that to your post ... in general, you should always add your work to your post). So, that is:
If Z is off, then X is on and Y is off
Now, this is almost the same as answer e) ... except in e) you have an 'or' rather than an 'and'
But, remember that in logic the 'or' is inclusive. So, if it is true that 'P and Q', then it follows that 'P or Q'.
Likewise, if Z is off, we know X is on and Y is off. But then it is also true that X is on or Y is off. So, if Z is off, then X is on or Y is off
So, the answer is e). e) is not logically equivalent to the original statement but, as we saw, it does logically follow from it, and that is what the question asked.
answered Dec 28 '18 at 14:53
Bram28Bram28
63.1k44793
$endgroup$
add a comment |
$begingroup$
From the comments, I gather you correctly found the contrapositive (you should really add that to your post ... in general, you should always add your work to your post). So, that is:
If Z is off, then X is on and Y is off
Now, this is almost the same as answer e) ... except in e) you have an 'or' rather than an 'and'
But, remember that in logic the 'or' is inclusive. So, if it is true that 'P and Q', then it follows that 'P or Q'.
Likewise, if Z is off, we know X is on and Y is off. But then it is also true that X is on or Y is off. So, if Z is off, then X is on or Y is off
So, the answer is e). e) is not logically equivalent to the original statement but, as we saw, it does logically follow from it, and that is what the question asked.
answered Dec 28 '18 at 14:53
Bram28Bram28
63.1k44793
$endgroup$
add a comment |
$begingroup$
From the comments, I gather you correctly found the contrapositive (you should really add that to your post ... in general, you should always add your work to your post). So, that is:
If Z is off, then X is on and Y is off
Now, this is almost the same as answer e) ... except in e) you have an 'or' rather than an 'and'
But, remember that in logic the 'or' is inclusive. So, if it is true that 'P and Q', then it follows that 'P or Q'.
Likewise, if Z is off, we know X is on and Y is off. But then it is also true that X is on or Y is off. So, if Z is off, then X is on or Y is off
So, the answer is e). e) is not logically equivalent to the original statement but, as we saw, it does logically follow from it, and that is what the question asked.
answered Dec 28 '18 at 14:53
Bram28Bram28
63.1k44793
$endgroup$
From the comments, I gather you correctly found the contrapositive (you should really add that to your post ... in general, you should always add your work to your post). So, that is:
If Z is off, then X is on and Y is off
Now, this is almost the same as answer e) ... except in e) you have an 'or' rather than an 'and'
But, remember that in logic the 'or' is inclusive. So, if it is true that 'P and Q', then it follows that 'P or Q'.
Likewise, if Z is off, we know X is on and Y is off. But then it is also true that X is on or Y is off. So, if Z is off, then X is on or Y is off
So, the answer is e). e) is not logically equivalent to the original statement but, as we saw, it does logically follow from it, and that is what the question asked.
answered Dec 28 '18 at 14:53
Bram28Bram28
63.1k44793
answered Dec 28 '18 at 14:53
Bram28Bram28
63.1k44793
answered Dec 28 '18 at 14:53
Bram28Bram28
63.1k44793
answered Dec 28 '18 at 14:53
Bram28Bram28
63.1k44793
63.1k44793
add a comment |
add a comment |
$begingroup$
Did you try to put this into a logical expression?
$endgroup$
– Bram28
Dec 28 '18 at 14:35
$begingroup$
actly the answer is e,but i dont know why
$endgroup$
– Kevin
Dec 28 '18 at 14:38
1
$begingroup$
@Kevin You correctly found the the contrapositive ....now think a little about what that says ... and you'll see how e) logically follows from that. That is, answer e) is not equivalent to the original statement, but it does logically follow from it
$endgroup$
– Bram28
Dec 28 '18 at 14:46
$begingroup$
@Bram28 im sorry, could u please be more detail oriented on how does it follow from it
$endgroup$
– Kevin
Dec 28 '18 at 14:46
$begingroup$
@Kevin remember the logical "or" is inclusive. So, if I tell you that snow is white and grass is green, does it follow (in logic) that snow is white or grass is green?
$endgroup$
– Bram28
Dec 28 '18 at 14:46