Group Theory


Q21.

The set {1, 2, 4, 7, 8, 11, 13, 14} is a group under multiplication modulo 15. The inverses of 4 and 7 are respectively:
GateOverflow

Q22.

In a room containing 28 people, there are 18 people who speak English, 15, people who speak Hindi and 22 people who speak Kannada. 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada whereas 13 persons speak both Kannada and English. How many speak all three languages?
GateOverflow

Q23.

Which of the following statements is FALSE?
GateOverflow

Q24.

Which one of the following is false?
GateOverflow

Q25.

The following is the incomplete operation table of a 4-element group. The last row of the table is
GateOverflow

Q26.

Let A be the set of all non-singular matrices over real number and let * be the matrix multiplication operation. Then
GateOverflow

Q27.

(G,*) is an abelian group. Then
GateOverflow