All dancers are performers(A) + All performers are singers(A) ⇒ All dancers are singers(A) ⇒ Some dancers are singers(I) ⇒ conversion ⇒ Some singers are dancers(I). All dancers are performers (A) + All performers are singers(A) ⇒ All dancers are singers(A) + No singer is a lyricist (E) ⇒ Some dancers are not lyricist (O). Hence, option 1 is correct. Some dancers are singers ⇒ conversion ⇒ Some singers are dancers(I). Some dancers are singers(I) + . No singer is a lyricist(E) ⇒ Some dancers are not lyricist (O). Hence, option3 is also correct. By elimination method - By option 2, we get, No + some = no definite conclusion between singer and dancer. Hence it is eliminated. By option 4, some + some = no definite conclusion can be drawn between singer and dancer. Hence it is eliminated. By option 1 and 3, the conclusion can be drawn. Hence answer is both 1 and 3.
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