Question:1. Rewrite each of the following in an English sentence and then explain if it is a true or false sentence.

a. 10 { x I x E N & x is odd}

b. 4 {4, 14, 17}

c. 0

d. 4 {4}

e. {14} {14}

2.Using the digits 0 through 9, find out how many 4-digit numbers can be configured based on the stated conditions:

a. The number cannot start with zero and no digits can be repeated.

b. The number must begin and end with an odd digit. (Repeated digits are okay.)

c. The number must be at least 5000 and be divisible by 10. (Repeated digits are okay.)

d. The number must be less than 3000 and must be even. No digits may be repeated in the last 3 digits. (That is, 2234 would be okay, but 2334 would not be okay.)

3.

a. The Mathematics Department at Sun Tan University is sending a delegation of mathematicians and graduate students to a conference. They will pay for 4 mathematicians and 5 graduate students to go. If the department has 16 mathematicians and 24 graduate students, how many different delegations are possible?

b. The mathematicians at Sun Tan University have published 14 research papers this year. The department chair wants to display them in the lobby. The display case can show 4 at a time. How many arrangements of 4 research papers are possible?