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Statements:All stations are trains.All trains are white.No white is red.Conclusions:I. No station is red.II. Only a few trains are red.
The least possible Venn diagram for the given statements is as follows:
Conclusions:
I. No station is red à It’s confirmed from the Venn diagram, hence true.
II. Only a few trains are red à Clearly, no train is red, hence false.
Thus, only I follows.
Statements:Most shops are closed.Most closed are open.Conclusions:I. Some shops are open.II. No shop is open.
I. Some shops are open à There is no direct connection between shop and open, hence it’s possible but not definite. So, the conclusion is false.
II. No shop is open à There is no direct connection between shop and open, hence it’s possible but not definite. So, the conclusion is false.
Thus, either I or II follows.
Statements:Only a few sharks are tigers.Some tigers are not lions.Some lions are panthers.Conclusions:I. Some panthers are sharks.II. Some panthers are tigers.
I. Some panthers are sharks à There is no direct connection between panther and shark, hence it’s possible, but not definite. So, the conclusion is false.
II. Some panthers are tigers à There is no direct connection between panther and tiger, hence it’s possible, but not definite. So, the conclusion is false.
Thus, neither I nor II follows.
Statements:At least some groups are not big.Some trees are big.Conclusions:I. All trees being groups is a possibility.II. All big being trees is a possibility.
I. All trees being groups is a possibility à There is no direct connection between trees and group. So, it’s possible, hence true.
II. All big being trees is a possibility à Some trees are big so, all big being trees is a possibility. It’s possible, hence true.
Thus, both I and II follow.
Statements:Only a few toys are boys.Some toys are not ploys.Conclusions:I. Some boys are not ploys.II. All ploys being boys is a possibility.III. Some toys are ploys.
I. Some boys are not ploys à There is no direct connection between boy and ploy. So, it’s possible, but not definite. Hence, the conclusion is false.
II. All ploys being boys is a possibility à There is no direct connection between ploy and boy. So, it’s possible, hence true.
III. Some toys are ploys à Some toys are not ploy but some toys can be ploys. So, it’s not definite, hence false.
Thus, only II follows.
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