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    36) 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 answer is E yet I feel that the 'OR' needs to be an 'AND'
    Why is E correct?
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    (Original post by dontrevisefail)
    36) 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 answer is E yet I feel that the 'OR' needs to be an 'AND'
    Why is E correct?
    Hi dontrevisefail


    Wow this is hurting my head! haha

    I feel that E is correct with 'or' not 'and' as in the statement is doesn't explicitly say that when bulb x is off y is also on, just that when one of them is, bulb z is on.

    Initially I was drawn to A being the correct answer, but I guess that it is just the original statement in a different order, and as the new statement must 'follow from this' it would make sense that is it E as the state of bulb Z has changed from on to off.

    Does this make sense? It did in my head, haha!

    Matt - NTU PG TSR Rep
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    (Original post by Postgraduate study at NTU)
    Hi dontrevisefail


    Wow this is hurting my head! haha

    I feel that E is correct with 'or' not 'and' as in the statement is doesn't explicitly say that when bulb x is off y is also on, just that when one of them is, bulb z is on.

    Initially I was drawn to A being the correct answer, but I guess that it is just the original statement in a different order, and as the new statement must 'follow from this' it would make sense that is it E as the state of bulb Z has changed from on to off.

    Does this make sense? It did in my head, haha!

    Matt - NTU PG TSR Rep
    Thanks Matt
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    (Original post by dontrevisefail)
    Thanks Matt
    Not a problem dontrevisefail!

    What's this for if you don't mind me asking?

    Matt
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    It's for the Cambridge economics entrance exam(ECAA)
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    (Original post by dontrevisefail)
    36) 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 answer is E yet I feel that the 'OR' needs to be an 'AND'
    Why is E correct?
    When you have a statement "if P then Q", then there's a logically equivalent statement called the contrapositive: "If (not Q), then (not P)".

    Here, the contrapositive is "If {bulb Z is off}, then {bulb X is on and bulb Y is off}. " (which I believe is what you deduced).

    So this statement does logically follow from what they give you, however it isn't on the list of options.

    but: {bulb X is on and bulb Y is off} certainly does imply {bulb X is on or bulb Y is off}.

    So the statement also implies E. E is a weaker condition than what could be deduced, but it still holds.
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    Thanks DFranklin, I get it now. How could I practice these?
    (Original post by DFranklin)
    When you have a statement "if P then Q", then there's a logically equivalent statement called the contrapositive: "If (not Q), then (not P)".

    Here, the contrapositive is "If {bulb Z is off}, then {bulb X is on and bulb Y is off}. " (which I believe is what you deduced).

    So this statement does logically follow from what they give you, however it isn't on the list of options.

    but: {bulb X is on and bulb Y is off} certainly does imply {bulb X is on or bulb Y is off}.

    So the statement also implies E. E is a weaker condition than what could be deduced, but it still holds.
 
 
 
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