Given below are three statements followed by three conclusions. Take the three statements to be true even if they deviate from commonly known facts. Statements: 1. All actors are musicians. 2. No musician is a singer. 3. Some singers are dancers. Conclusions: 1. Some actors are singers. 2. Some dancers are actors. 3. No actor is a singer. Use only the following predicates: Actor(x), Musician(x), Singer(x), and Dancer(x). The domain is the set of all people, which you may omit in your statements. (a) Write the quantified statements for statements (2) and (3). Statement (1) has been done for you: vx(Actor(x) Musician(x)). (b) Three conclusions are given. Identify the only one that is valid from the three statements, and explain why it is so