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The question has a set of four statements. Each statement has three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.

1. No cowboys laugh. Some who laugh are sphinxes. Some sphinxes are not cowboys.
2. All ghosts are florescent. Some ghost do not sing. Some singers are not florescent.
3. Cricketers indulge in swearing. Those who swear are hanged. Some who are hanged are not cricketers.
4. Some crazy people are pianists. All crazy people are whistlers. Some whistlers are pianists.
1. ​A and B
2. C only
3. A and D
4. D only

these type of questions we can solve using either venn diagram or deduction rules , for 2 premises and conclusion type questions can easily solve by deduction rules ...

these are the following rules

1. every deduction must contain 3 distinct terms

2. middle term must be distributed atleast once in the premises and middle term never contain in conclusion

here middle term means linking term of 2 premises or we can say common term in both premises and distributed term means a set is said to be distributed if we can account (some atleast info about elements of set) for all the alements of that set .for more detail about distribution (http://www.indiabix.com/logical-reasoning/logical-deduction/formulas

there mainly 4 type of premises in which following terms are distributed

2.1 universal affermative eg : all A are B . here A term is distributed and B is not distributed

2.2 particular affermative eg: some A are B . here both A and B are not distributed terms

2.3 unversal negative eg : NO a is B , here both A and B are distributed terms .

2.4 particular negative eg : some A are not B , or all A are not B  , here A is not distributed and B is distributed .

3 . if one premise is particular then conclusion if any must be particular .

4. if one premise is negative then conclusion if any must be negative

5.if both premises are negative ,  then no conclusion

6.if both premises are particular , then no conclusion

7 . if a term is not distributed in premises then it cant be distributed in conclusion .

now option A ) premise 1 . No cowboys laugh  , here cow boy is distributed term and laugh is also distributed from rule (2.3)

premise 2 . Some who laugh are sphinxes , here laugh and sphinxes both are not distributed rule (2.2

so here middle term laugh should be distributed once which is true here , so conclusion should be  from rule 3,4 particular and negative , so it must be some sphinxes are not cowboys .. it is also following 7 rule which says "if a term is not distributed in premises then it cant be distributed in conclusion"  so sphinxes is not distributed in premise and in conclusion , its not distributed so option A ) is correct .

option B) premise 1. All ghosts are florescent  , ghost distributed and florescent is not distributed (2.1)

premise 2.Some ghost do not sing  , ghost not distributed , and sing is distributed(2.4

given conclusion  Some singers are not florescen , which is not correct bcoz it does not follow 7th rule , florescen is not distributed in premise so it must not be distributed in conclusion but here (according to 2.4 type ) florescen is distributed so it is false .

option C) premise 1. Cricketers indulge in swearing  , here cricketers are distributed , swearing not distributed (2.1)

premise 2. Those who swear are hanged

given conclusion " Some who are hanged are not cricketers." which particular negative but no premise is negative so conclusion should not be in negative(rule 3,4 ) so its false

option D ) premise 1. Some crazy people are pianists  , here crazy not  distributed , pianists not distributed

premise 2 . All crazy people are whistlers , here crazy distributed , whistlers not distributed

given conclusion :Some whistlers are pianists.  which is correct , it follow all deduction rules .

hence A and D are correct so ANS is C)

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Good Explaination
Thank you :)