Q: In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values "true" and "false", usually denoted 1 and 0 respectively. Instead of elementary algebra where the values of the variables are numbers, and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction "and" denoted as , the disjunction "or" denoted as , and the negation "not" denoted as . It is thus a formalism for describing logical relations in the same way that ordinary algebra describes numeric relations.

Boolean algebra was introduced by George Boole in his first book "The Mathematical Analysis of Logic" (1847), and set forth more fully in his "An Investigation of the Laws of Thought" (1854). According to Huntington, the term "Boolean algebra" was first suggested by Sheffer in 1913.

Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.

Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields. In an abstract setting, Boolean algebra was perfected in the late 19th century by Jevons, Schroder, Huntington, and others until it reached the modern conception of an (abstract) mathematical structure. For example, the empirical observation that one can manipulate expressions in the algebra of sets by translating them into expressions in Boole's algebra is explained in modern terms by saying that the algebra of sets is "a" Boolean algebra (note the indefinite article). In fact, M. H. Stone proved in 1936 that every Boolean algebra is isomorphic to a field of sets.

1. George Boole

Numbered questions:
1. what did George Boole Introduce?

input: Make use of the article to answer the questions. "Angie, I know you like to sing," her father, a worker, told Angela Brown, "but you must have something to fall back on ."

Brown took her father's advice. She got a degree in secretarial science before entering Oakwood College, in Huntsville, Alabama. However, her aim was to become a singer at religious meetings. So after graduation she headed for Indiana University to study with the famous soprano Virginia Zeani.

Once, when Brown was troubled by self-doubt, Zeani said to her, "If you want to be the next Aretha Franklin, you need no more lessons," Brown remembers her saying. "But if you want to be the best Verdian soprano this world has ever seen, you must work."

Work she did. Three times she competed in the Metropolitan Opera National Council Auditions . Three times she failed to make the final round in New York. Then, in 1997 at age 33, the age limit for sopranos to audition, she gave it one more try. She signed up at the last minute and didn't even practice, thinking, "All they could do was to tell me no, and that didn't hurt my feelings anymore." She had the strength she needed to fall back on if she failed.

She won. But making it in New York was just the beginning. It took her three more years to become an understudy at the Met. But waiting in the wings was fine with her. Finally, her time came. When the featured singer fell ill, Brown earned the chance to sing the lead role in Aida. And The New York Times described her performance as a great success. Angela Brown, who had prepared for 20 years, was an "overnight" successful singer at age 40. 1. Who got a degree?
2. Had someone suggested she do so?
3. Who?
4. What had she liked to do?
5. What school did she attend?
6. Did she go to work after graduating?
7. Where did she go?
8. Who did she study with while there?
9. What was she known for?
10. Did Brown also want to be a soprano?
11. What kind?
12. How many times did she audition?
13. How many times was she rejected?
14. Did she try again?
15. Could she keep trying every year for as long as she wished to?
16. Why not?
17. And how old was she?
18. So this would be her last chance?
numbered_answers: 1. Angela Brown
2. yes
3. her father
4. sing
5. Oakwood College
6. no
7. Indiana University
8. Virginia Zeani.
9. she was a famous soprano
10. yes
11. Verdian
12. three
13. three
14. yes
15. no
16. the age limit for sopranos was 33
17. 33
18. yes

(CNN) -- Martina Hingis and Anna Kournikova will team up again to play at this year's Wimbledon championships.

The popular pair won the 1999 and 2002 Australian Open doubles titles, but will be returning the SW19 to play in the legends doubles event for players who are retired from the professional circuit, the management company Octagon said Tuesday.

Swiss star Hingis won five grand slam singles crowns and nine in doubles during a glittering career which ended under a cloud in 2007, when she was suspended for two years for testing positive for cocaine at Wimbledon.

The 29-year-old denied taking the drug, but did not appeal the ban, which ended last September, prompting speculation that she may attempt a return to the WTA circuit.

Kournikova is a year younger, but has not played regularly on the main tour for seven years after being hit by a string of injuries.

The Russian, who reached a career-high of number eight, made it to the semifinals of the singles at Wimbledon in 1997, but grand slam success eluded her.

The pair were once labeled as the 'Spice Girls' of tennis, with the height of their fame coinciding with the peak of popularity of the British all-girl band, which included David Beckham's wife Victoria.

As well as winning two grand slam titles together, the pair also reached No.1 in the WTA doubles rankings.

"I'm so excited to be returning to the UK to play doubles with Martina again," Kournikova told her official Web site.

"This tournament has always held a special place in my heart, and it will be a great honor to play on the courts of Wimbledon again. I'm looking forward to having a lot of fun." What are the answers to this following set of questions: 1. What drug did Hingis use?
2. When was she caught?
3. How?
4. How old was she?
5. Was she punished?
6. With what?
7. For how long?
8. Who is her teammate?
9. How old is she?
10. Where will they be playing?
11. In which event?
12. What title have they won?
13. When?
14. What event is for retirees?
15. How many grand slam singles did Hingis win?
16. What about Kournikova?
17. How many times did she play in singles semifinals at Wimbledon?
18. What year?
19. What were they nicknamed?
20. Who's wife was in the Spice Girls band?
Answer:
1. cocaine
2. 2007,
3. she tested positive
4. 29
5. Yes
6. Suspension
7. two years
8. Anna Kournikova
9. 28
10. Wimbledon
11. Wimbledon championships.
12. Australian Open doubles
13. 1999 and 2002
14. legends doubles event
15. eight,
16. eight,
17. five
18. 1997,
19. Spice Girls
20. David Beckham