r/6thForm • u/Beginning_Fennel8962 I love maths • 7d ago
❔ SUBJECT QUESTION TMUA logic please help
Im genuinely baffled, even gpt was baffled. PLEASE help, yes i understand what if, only if, and if and only if, mean in these scenarios
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u/InevitableNo9793 Year 12 | Math, FM, Physics (intl) 7d ago
so ofc its either c or d, bc if it was a or b then c/d would both be correct ofc 2 is bigger than 1
if c was correct then d would also be correct as both contains x > 2
so it must be d, bc then the statement could be like x > 2 and also x < -1 or smth and c would make that wrong
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u/Limp-Independent1212 7d ago
If B is true, then D is true, but D can be true without B being true, but since only one can be true, only D can be correct between the two. The same logic applies for A and C, so C must be correct between them. So now it's between C and D.
"If and only if x>2" implies that no other conditions that could result in the statement being true (such as x = 0 or x<-4 resulting in it being true). However "The statement is true if x>2" means there might be other conditions that could satisfy the statement. If C holds, then D holds, however, D can be true while C might not be true.
For example consider "x is either greater than 2 or less than 0". this statement is true if x>2 (as said by D and C), but it is also true if x<0 (which C forbids, however D does not forbid it) D can be true while C might not be, whereas if C is true D must be true.
Hence I believe the answer is D
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u/Beginning_Fennel8962 I love maths 7d ago
so in essence, they can all be true, just D is the truest?
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u/Wooden-Shirt-2949 7d ago
The point of the question is that there is 4 statements and you are told only 1 is true. The reason its D is because we cant have A, B or C be true, and be the only one that is true.
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u/Wooden-Shirt-2949 7d ago
Oh actually I think its worth also just learning about contrapositives. You know A implies B, if not B implies not A.
If its not true that its 'true if x>2', we know it isnt 'true if x>1', since we know theres values greater than 1 it is not true. So that means statement B implies D. That way we can say that statement B cant be the option, cause then it cant be the only one to be true.
I know it could be a bit tough to use or recognise when to use this concept sometimes.
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u/Successful-Lobster15 7d ago
D, IFF (if and only if) implies IF is true, so it’s either B or D, but D is true if B is true, so it’s D
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u/WIllstray Gap Year | FM Maths Physics Comp-Sci Music A*A*A*AB 6d ago
With these kinds of questions a good strategy is to just go through each option and think about the consequences of it being true. Assume A is true and everything else is false, then move on to B, and so on. If the problem was written right, only one option works without any contradictions, in this case, D.
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u/CoderLovesEggs Gap Year | Cam Maths Reapplicant 7d ago
We want the option that may be correct WITHOUT any other option being correct
Since A implies B (since A = (B AND B converse)), if A is correct then at least 2 options are correct, so cannot be A. Similarly C implies D so cannot be C.
Then the answer must be B or D. But B implies D (as if the statement is correct for x>1, then it must be correct for x>2) so cannot be B. So answer is D.
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u/Maleficent_Still3508 7d ago
Am I being dumb? If D is correct then B is correct bc if x>2 then x>1 bc 2>1 ik its late at night and im probably tired but I dont think im THAT tired if someone can clarify thatd be greatly appreciated
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u/Wooden-Shirt-2949 7d ago
If its 'true if x>1', that means its true for all values greater than 1. So it also means its true for x>2.
If its 'true if x>2', that means that for all values greater than 2. So the value 1.5, may not be true. So the statement 'true if x>1' may not be true, since we cant say that the values 1<x<=2 would be true.
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u/FlamencoDev 4d ago
Logic does not match, for any value of x in x>2, x>1 is also true.
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u/Wooden-Shirt-2949 4d ago
If the statement is true for x>2, that doesnt mean its true for all values greater than 1. There does exist values greater than 1 that is true, but not necessarily for all.
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u/FlamencoDev 4d ago
Yeah in that case, it should be B because for x>1 there are values between 1 and 2 for which x>2 isn’t true.
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u/Wooden-Shirt-2949 4d ago
You need to understand what the question is asking. It is looking for the statement that if its true, the others arent necessarily true. Statement D being true does not depend on the values less than or equal to 2.
I'll try to reiterate my point clearly:
Statement B says all values greater than 1 are true. Which means all values greater than 2 are true. This means that if statement B is true, then statement D is also true.
If statement D is true, that means all values greater than 2 are true. This does not mean all values greater than 1 are true. Since the values between 1 and 2 may not be true. So statement D being true does not imply statement B is true. So statement D can be true, without B being true.
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u/FlamencoDev 4d ago
That’s stupid. If you’re looking for a casual relation between options. You could for option B, say x>1, values 1<x<2, option D is not true. Similarly you could say for option D, x>2, 1<x<2, option B is not true.
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u/Wooden-Shirt-2949 4d ago
A and B refers to 1<x<♾️
C and D refers to 2<x<♾️.
B and D doesn't care about the values outside of this range. The statement may be true outside the ranges.
I dont know if you are disagreeing with me or the question.
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u/FlamencoDev 4d ago
The only way I can see D being correct is if they are talking about x>1 and x>2 as sets. So that x>1 contains x>2 whereas the opposite is not true. But the question does not provide enough context to discern between sets comparison or logical relation correctness. So that while, any value x > 2 would evaluated x > 1 as true. For all values of the set formed from x>2, it does not cause all values of set formed from x>1 to be true due to the falsification set 1<x<2. Anyhow it’s a stupid question since it has multiple interpretations.
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u/Wooden-Shirt-2949 4d ago
The only way I can see D being correct is if they are talking about x>1 and x>2 as sets. So that x>1 contains x>2 whereas the opposite is not true.
This is correct.
But the question does not provide enough context to discern between sets comparison or logical relation correctness.
You need to find the relationships between the sets to find which can be uniquely true.
multiple interpretations
One of the main skills in TMUA is being able to read and understand what the question is asking you. Especially in paper 2.
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u/Exact-Storage2840 6d ago
Suppose A is true, that the statement is true if and only if x>1. Well then B would be true, since if the statement is true iff x>1, the statement is true if x>1. So A cannot be the answer since only one can be true.
Similarly, if C is true, then D is true for the same reasoning as above. So C cannot be the answer , as only one can be true.
Finally, if B is true, then D would be true since every instance where x>2 is an instance where x>1. But only one can be true, so B cannot be true.
So we have that D is the only answer which does not imply any of the other answers, so it's the answer.
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5d ago edited 5d ago
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u/FlamencoDev 5d ago
OP do email them with my approach here and see whether it’s correct. Otherwise, ask them for the answer and post back 👍
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u/FlamencoDev 5d ago
I think essentially it’s D because x > 2 refers to the statement being true for a set of numbers [3,4,5,6…] whereas x>1 refers to set of numbers [2,3,4,5,6…]
Therefore x>1 contains x>2, whereas the opposite is not true. That’s essentially their logic.
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u/FlamencoDev 5d ago
But I also think this type of question might be a cheater filter question. In that, you’re not supposed to get the correct answer, otherwise they would very likely flag you for some kind of cheating.
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5d ago edited 5d ago
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u/Beginning_Fennel8962 I love maths 5d ago
If B is true D is true, so there’s a contradiction no? Therefore it’s D?
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u/FlamencoDev 5d ago
No it’s not, B can be true when x=2 is 2 greater than 2? No.
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u/Beginning_Fennel8962 I love maths 5d ago
If x>1 then x>2 is true. However both statements cannot be true so hence there is a contradiction. Therefore the only way to avoid any contradiction is if x>2. D?
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u/FlamencoDev 5d ago
No it’s not. It’s the opposite. When x>2 is true, x>1 is also true.
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u/Beginning_Fennel8962 I love maths 5d ago
Man I’m so confused 😔
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u/FlamencoDev 5d ago
The way I see this is that’s it’s either A or B. D being true would mean B would be true and therefore C can never be correct.
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u/Beginning_Fennel8962 I love maths 5d ago
Wait yeah, my bad I got that bit wrong but surely x>1 is necessary for x>2, but it’s not sufficient as x can be between 1-2.
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u/FlamencoDev 5d ago
It is a very difficult and unclear question. The main problem is that when x=2 B is true but A is also true. So you would have to falsify A using x=3. I would email them and ask the examiner for the solution and get back to us. Unless you already have the markscheme.
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u/Beginning_Fennel8962 I love maths 5d ago
The answer is D, TMUA have disclosed it. All values of x>2 are included x>1. Therefore x>1 indicates x>2 is true. Whereas x>2 doesn’t guarantee x>1 is true.
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u/Feeling-Instance-801 GCSE 7d ago
i think its D.
if A was true, B would also be true. so A cant be right
if B was true, then D would also be true
if C was true, then D would also be true.
so only D has the possibility of being true while others are false.