2. Valid starts: a,c,d,f

    Invalid starts: b,e,g,h. It's okay if you included b as not the start of valid start.

    Starts with extraneous statement(s) or phrase(s): i,j.

3. c,d,f,g

4. b,c. (Notation introduced in an if-then statement, or introduced with a "for all" quantifier, does not survive past the end of the sentence with that if-then or quantification phrase. In choice 'a', x no longer has any meaning by the start of the second sentence, so cannot be used to define y. In the second sentence of choice 'd', there is no surviving object called y about which any statement can be made.)

5. f

6. a: False

    b: True

7. a: False

    b: True