is the intersection of two sets,  and .  itself is the intersection of , the set of persons who like The Rolling Stones, and , the set of persons who like Alanis Morissette.  is the set of persons who like Bob Seger, so , the complement of , is the set of persons not in  - that is, persons who dislike Bob Seger.

Therefore, anyone in the set  likes The Rolling Stones, likes Alanis Morissette, and dislikes Bob Seger. The correct choice is "John likes The Rolling Stones and Alanis Morissette, but he dislikes Bob Seger."

First, we note that the total number of seating arrangements for eight people is 

The number of arrangements that would have Steve and Jim in adjacent seats would be calculated as follows:

The number of ways to choose two adjacent seats is eight: 1-2, 2-3, and so forth up to 8-1. Multiply this by 2, since each choice has two different orders for Steve and Jim. Multiply this by 

,

the number of ways the remaining six persons can be seated. This makes

seating arrangements with Steve and Jim together. Since this is not desired, subtract this from the total number of arrangements:

This is the number of arrangments without Steve and Jim together, and it is the correct choice.

By DeMorgan's Law,

That is, the complement of the union of two sets is the intersection of their complements. 

Also, the complement of a complement of a set is the set itself, so  and . Therefore, 

.

Consequently, we are looking for a number that falls in the intersection of  and . The number must be both prime and odd. 2 and 4 are eliminated for being even. 1 is not considered a prime number, having only one factor. 3, which has only two factors, 1 and 3, is prime, and is the correct choice.

A number that is divisible by 44 must also be divisible by all factors of 44.

One factor is 4. The number is divisible by 4 if the last two digits form a number itself divisible by 4. Since the last two digits are "12", which is divisible by 4, we know the number to be divisible by 4 regardless of the digit chosen.

Another factor is 11. The number is divisible by 11 if and only of the alternating sum has an absolute value divisible by 11. If  is the missing digit, then 

.

We can set each of the choices equal to and see which one works:

Only in the case is the alternating sum divisible by 11, so this is the correct choice.

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

We can see that Tucson is  warmer than New Castle.

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

We can see that Tucson is  warmer than New Castle.

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

We can see that Tucson is  warmer than New Castle.

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

We can see that Tucson is  warmer than New Castle.

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

We can see that Tucson is  warmer than New Castle.

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

We can see that Tucson is  warmer than New Castle.