91Ó°ÊÓ

The given statement: 'It is the case that Sondheim and Picasso are both not musicians.' is formulated by using a NEGATION of an AND statement. An AND statement is only true if both components are true, and a negation makes the original statement false. Thus, the given statement is saying that 'NOT (Sondheim is a musician AND Picasso is a musician).' The negation of an AND statement is equivalent to a statement using the operator OR, that is: 'Sondheim is not a musician OR Picasso is not a musician.'

Option a. 'Sondheim is not a musician or Picasso is not a musician.': This is equivalent to the given statement as per the logic rules mentioned above. Option b. 'If Sondheim is a musician, then Picasso is not a musician.': This is also equivalent to the original statement because it implies that if Sondheim is a musician, then it's not true that Picasso is also a musician, hence they cannot be both musicians. Option c. 'Sondheim is not a musician and Picasso is not a musician.': This statement is not equivalent to the original statement - it's a statement using the operator AND and implies that both Sondheim and Picasso are not musicians, which is more restrictive than the original statement. Option d. 'If Picasso is a musician, then Sondheim is not a musician.': This statement is again equivalent to the original statement as it's the reverse condition of option B.

Based on the evaluation, the option not equivalent to the original statement is c. 'Sondheim is not a musician and Picasso is not a musician.' as it makes a stronger claim than the original statement.