Home
Class 12
MATHS
A binary operation * on the set {0,1,2,3...

A binary operation `*` on the set {0,1,2,3,4,5} is defined as
` a*b= {{:(a+b, "if" a+b lt 6),(a+b-6, "if" a +b gt=6):}`
Find the composition table for `*` Also, show that zero is the identity for this operation and each non-zero element a of the set is invertible with 6-a, being the inverse of a.

Text Solution

Verified by Experts

The correct Answer is:
(i) `a** 0 = 0 ** a = a`. Hence, `0` is the identity for an operation.
(ii) `6 - a` is its inverse.
Promotional Banner

Topper's Solved these Questions

  • VERY SIMILAR TEST 5

    ARIHANT PRAKASHAN|Exercise SECTION C|12 Videos

  • VERY SIMILAR TEST 5

    ARIHANT PRAKASHAN|Exercise SECTION C|12 Videos

  • VERY SIMILAR TEST 4

    ARIHANT PRAKASHAN|Exercise Section - C |13 Videos

  • VERY SIMILAR TEST 6

    ARIHANT PRAKASHAN|Exercise SECTION C ANSWER ANY ONE QUESTIONS|11 Videos

Similar Questions

Explore conceptually related problems

Consider the binary operation * on the set {1,2,3,4,5} defined by a**b = min{a,b}. Write operation table of operation *.

Consider the binary operation * on the set{1,2,3,4,5}defined by a*b=min(a,b). Write operation table for operation *.

Consider the binary operation ** on the set {1, 2, 3, 4 5} defined by a ** b = min (a, b). Write operation table of operation ** .

Consider the binary operation ** on the set {1, 2, 3 , 4, 5} defined by a**b=min {am b} . Write the operation talbe of operation ** .

Consider the binary operation on the set {6, 7, 8, 9, 10), defined by a*b = min (a, b}. Write operation table of operation *.

If the binary operation on the set of integers Z, defined by a b= a +3b^(2) , then find the value of 8*3.

If the binary operation ** on set of integers Z is defined as a**b=a+3b^2 then find the vlaue of 2**4 .

If * is binary operation on set Q of rational numbers defined as a**b=(ab)/(5) . Write the identity for *, if any.

ARIHANT PRAKASHAN-VERY SIMILAR TEST 5-SECTION B
  1. A binary operation * on the set {0,1,2,3,4,5} is defined as a*b= {{...

    Text Solution

    |

  2. Discuss the commutativity and associativity of binary operation .*. d...

    Text Solution

    |

  3. Directions (Q. Nos. 27 and 28) Solve the following equations: "tan"...

    Text Solution

    |

  4. Answer any three questions (d) Solve the following LPP graphically M...

    Text Solution

    |

  5. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

    Text Solution

    |

  6. A die is rolled until a 6 is obtained. What is the probability that ...

    Text Solution

    |

  7. Let A=[{:(2,-1),(3,4):}],B=[{:(5,2),(7,4):}]andC=[{:(2,5),(3,8):}]. F...

    Text Solution

    |

  8. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

    Text Solution

    |

  9. The probability that A hits a target is 1/3 and the probability that B...

    Text Solution

    |

  10. If A =[[1,2,2],[2,1,2],[2,2,1]] then prove that A^2-4A-5I=0.

    Text Solution

    |

  11. Verify Rolle.s theorem for the function f(x)=x^(2)-3x+2 in the interva...

    Text Solution

    |

  12. If x=cos^-1(1/(sqrt(1+t^2))), y=sin^-1(1/(sqrt(t^2+1))) then dy/dx is ...

    Text Solution

    |

  13. Find the equation of the normal at a point on the curve x^(2) = 4y, wh...

    Text Solution

    |

  14. Find (dy)/(dx), if y = k tan^(-1) ((y)/(x)).

    Text Solution

    |

  15. Determine the interval in which the function f(x) = x^3-5x^2+3x+97 is ...

    Text Solution

    |

  16. Reduce x (dy)/(dx) + y = xy^(3) to linear differential equation.

    Text Solution

    |

  17. Evaluate int [ (1)/( "In" x ) - (1)/(("In" x)^2) ]dx.

    Text Solution

    |

  18. Find the differential equation for the family of curve y= a sin^(-1) x...

    Text Solution

    |

  19. Solve (dy)/(dx) = e^("sin"^(-1) x). (sin^(-1) x)/( sqrt(1-x^(2) ).

    Text Solution

    |

  20. Find the area bounded by the curve y=2 x -x^(2) and the straight line ...

    Text Solution

    |