Assume both statements are true. If  is the number of students enrolled in both courses, we can fill in the Venn diagram for the situation with the expressions shown:

No further information is given in the problem, however, so there is no way to calculate .

The question asks for the number of students in the set , where  and  are the sets of students who took French and Creative Writing, respectively.

From Statement 1 alone, a Venn diagram representing this situation can be filled in as follows:

It is known that ; subsequently, . But no other information is given, so , the desired quantity, cannot be calculated.

From Statement 2 alone, a Venn diagram representing this situation can be filled in as follows:

Again, no further information can be computed.

Now assume that both statements are true. Then it follows from Statement 1 that , and it follows from Statement 2 that the desired quantity is 

.

The question asks if Cary is an element of .

Assume Statement 1 alone. From the Venn diagram, it can be seen that  and  are disjoint sets. Since Cary is an element of , he cannot be an element of  - Cary is not a Male.

Assume Statement 2 alone. From the Venn diagram, it can be seen that  - that is, if Cary is an element of , then she is an element of . Restated, if Cary is a Male, then he is a Teenagers. The contrapositive also holds - if Cary is not a teenager - which is given in Statement 2 - then Cary is not a male.

The question is whether or not Jamie is an element of .

Assume both statements to be true. Then Jamie is an element of the set , shaded in this Venn diagram:

Some elements of  are elements of , but some are not, making the two statements together insufficient to answer the question of whether Jamie is an element of . Whether Jamie was born in an even month or not cannot be determined.

 is the intersection of , the complement of the set of people who like cheddar cheese - that is, the set of people who don't like cheddar cheese - and , the set of people who like Swiss cheese. For  to be true, it must hold that Gina doesn't like cheddar cheese and Gina likes Swiss cheese. Either statement alone makes this false.

Assume Statement 1 alone.  is the intersection of two sets -  and , the complements of, respectively, the set of people who like The Eagles and the set of people who like Bruce Springsteen. Equivalently, this is the intersection of the set of people who do not like The Eagles and the set of people who do not like Bruce Springsteen. Since , Holly falls in both sets. Specifically, she does not like The Eagles.

Assume Statement 2 alone.  is the union of two sets - , the set of people who do not like The Eagles and , the set of people who like Crosby, Stills, and Nash. If , Holly falls in either or both sets, so either she doesn't like The Eagles, or she likes Crosby, Stills, and Nash, or both. It is not resolved whether she likes The Eagles or not.

Assume both statements to be true.

 is the union of the sets , , and ; Veronica falls in this union, so she falls in at least one of the three sets, so she likes one, two, or all three of Pearl Jam, Nirvana, and Soundgarden.

Similarly, from Statement 2, Veronica falls in at least one of the three sets , , and  - the complements of the three sets - meaning that she doesn't like at least one of the three. Therefore, Veronica likes none, one, or two of the artists.

From the two statements together, it follows that Veronica likes one or two of the artists. Without further information, however, it cannot be determined whether she likes two of the artists.

 is the union of the set , the set of all people who like coffee, and , the complement of the set of all people who like tea - that is, the set of all people who do not like tea.  if either Frank likes coffee or Frank does not like tea or both. 

Statement 1 alone, that Frank likes tea, does not prove or disprove this to be true true; if Frank likes coffee, then this is true, and if he does not like coffee, then this is not true. Statement 2 alone, however, proves this statement true.

 and .

This can be respresented in a Venn diagram as follows:

Assume both statements to be true. If we let  represent Bumpy, then from the diagram, it can be seen that if Bumpy is neither a Bee or a Dee, it is possible for Bumpy to be be a Fee or to not be a Fee.

Let  be the sets of Fe's, Fi's, Fo's and Fum's, respectively. According to the premise of the problem, the sets  and  are disjoint (they have no elements in common); the sets  and  are disjoint; and the sets  and  are disjoint. No other relationships are known. A Venn diagram of these relationships is below:

Assume both statements to be true. The question is whether or not Jack falls in set . If Jack is neither a Fi nor a Fo, then Jack falls in neither set  nor set . As evidenced by the two X's in the diagram, it is possible for Jack to fall in set  or to not fall in set . Therefore, the question of whether Jack is a Fum is unresolved.