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)