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# Sufficient and Necessary Question watch

1. 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?
2. (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
3. (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
4. (Original post by dontrevisefail)
Thanks Matt
Not a problem dontrevisefail!

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

Matt
5. It's for the Cambridge economics entrance exam(ECAA)
6. (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.
7. 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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Updated: October 27, 2017
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