Plincks, Ploncks, Pluncks!

Logic Level 1

All plinks are plonks.
Some plunks are plinks.

Which of the statements X, Y, Z below must be true?

X : All plinks are plunks.
Y : Some plonks are plunks.
Z : Some plinks are not plunks.

X Y Z None of these

Satyajit Mohanty by Satyajit Mohanty , 24, India

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1 solution

Chung Kevin
Jul 28, 2016

From the first given statement, since all plinks are plonks , then the set of plinks is a subset of plonks. So, the Venn diagram that illustrate this first statement should look like the diagram above.

From the second given statement, since some plunks are plinks , then it is possible that all plunks are plinks , or all plinks are plunks as well. So we got 4 possible Venn diagrams, as shown below.

So, for any of "X", "Y', "Z" to be true, we can check against each of these diagrams.

X - It is not true in (1), so statement X can be false.

Y - It is true in all these diagrams.

Z - It is not true in (4), so statement Z can be false.

Hence, only statement Y can be true.

27 Helpful 5 Interesting 2 Brilliant 6 Confused

I think what you did here would be more clearly expressed as showing that it is not necessary from the statements given to conclude any of statements X or Z is true or false.

For any of the statements X , Y , Z to be affirmed as true it should be showed that they are necessarily true which can't be said for X , Z (on the ground of your argument) and the conclusion should be rather that from the information given above ,"Y must be true" and not that "Y can be true" as said by you in the last paragraph anyway.

A A - 4 years, 10 months ago

Some plinks are not plunks

Chris Rather not say - 3 years, 9 months ago

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We do not know that for certain. That is not a true statement in case (4).

Chung Kevin - 3 years, 9 months ago

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Oh yeah :\

Chris Rather not say - 3 years, 9 months ago

there is a fifth case diagram not shown. For that diagram, Y is false.

gerardo katz - 2 years, 10 months ago

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Can you elaborate on how Y could be false?

What is the fifth case diagram that you're thinking of?

Chung Kevin - 2 years, 10 months ago

This seems incorrect. From the statement "All Plinks are Plonks" it doesn't follow necessarily that some plonks are plunks. You can have a scenario where all plinks are plonks and no plonk is plunk. Just draw a circle representing plonks outside the circle representing plunks.

Pedro Alvares - 2 years, 7 months ago

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From the statement "All Plinks are Plonks" it doesn't follow necessarily that some plonks are plunks

I agree that just the first statement is insufficient to conclude that "some plonks are plunks". We have to use the second statement of "Some plunks are plinks."

You can have a scenario where all plinks are plonks and no plonk is plunk. Just draw a circle representing plonks outside the circle representing plunks.

Again, we could do so if we only had the first statement of "All Plinks are Plonks". However, you can see that the second statement of "Some plunks are plinks." would directly contradict your claim of "Just draw a circle representing plonks outside the circle representing plunks." The plunk circle, being outside the plonk circle, cannot intersect the plink circle that is contained within the plonk circle.

If you're not convinced, can you draw up the exact scenario that you're describing?

Chung Kevin - 2 years, 7 months ago

I think it would be more clear if you were to say "at least some plonks are plunks"

Samuel Cramer - 2 years, 5 months ago

Why the 4th venn diagram is correct?

Maunil Chopra - 2 years, 2 months ago

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