Home
Class 12
MATHS
Number of binary operations on the set {...

Number of binary operations on the set `{a, b}` are (A) 10 (B) 16 (C)20 (D) 8

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|132 Videos

  • THREE DIMENSIONAL GEOMETRY

    V PUBLICATION|Exercise QUESTION BANK|103 Videos

Similar Questions

Explore conceptually related problems

The number of binary operations that can be defined on the set A = {a, b, c} is : a) 3^(3) b) 3^(4) c) 3^(9) d) 9^(3)

Let * be a binary operation on N , the set of all natural numbers defined by a * b = a^b , a, b in N . Is (N,*) associative or commutative?

Consider the binary operation ast on the set R of real numbers, defined by aastb = a b / 4 Find the inverse of 5.

Consider the binary operation ast on the set R of real numbers, defined by aastb=a b /4 Show that ast is commutative and associative.

Let A=N xx N and let * be a binary operation on A defined by (a, b) * (c, d) = (a c, b d) show that (i) ( A ,*) is associative (ii)( A ,*) is commutative

Let ** be a binary operation on the set Z of integers as a**b=a+b+1 . Then find the identity element:

Let ast be a binary operation on the set of all real numbers R defined by aastb=a+b+a^2b for a, b belongs to R. Prove that ast is neither commutative nor associative.

Let ast be a binary operation on the set of all real numbers R defined by aastb=a+b+a^2b for a, b R. Find the identity elements in R if exists.

V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Let f:RrarrR be defined as f(x) = 10x+7 Find the function g:RrarrR s...

    Text Solution

    |

  2. Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 i...

    Text Solution

    |

  3. If f:RrarrR is defined by f(x) = x^2-3x+2, find f(f(x))

    Text Solution

    |

  4. Show that the function f:R rarr R given by f(x)=x^3 is injective.

    Text Solution

    |

  5. Given a non empty set X, consider P(X) which is the set of all subsets...

    Text Solution

    |

  6. Find the number of all onto functions from the set {1,2,3 …... n}to i...

    Text Solution

    |

  7. Let S={a, b, c} and T={1,2,3}, Find F^-1 of the following functions F ...

    Text Solution

    |

  8. Let A={-1,0,1,2,} B={-4,-2,0,2} and f, g: A rarr B be functions define...

    Text Solution

    |

  9. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)20 ...

    Text Solution

    |

  10. Show that the relation R on the set N xx N defined by (a, b)R(c, d)...

    Text Solution

    |

  11. If f: R rarr R be a function defined by f(x)=4 x^3-7, show that the fu...

    Text Solution

    |

  12. Consider the binary operation ast : QtoQ where Q is the set of rationa...

    Text Solution

    |

  13. Prove that the function f: Q rarr Q given by f(x)=2 x-3 for all x in Q...

    Text Solution

    |

  14. Prove that the function f: N rarr N , defined by f(x)=x^2+x+1 is one-...

    Text Solution

    |

  15. Let f: R rarr R be a function defined by f(x)=x^2-3 x+2 Find f^' (2) a...

    Text Solution

    |

  16. If f : R rarrR be defined by f(x) = 5x - 3, then prove that f is one-o...

    Text Solution

    |

  17. Let f, g: R rarr R be defined by f(x)=x^2+1and g(x)=sin x. Find f o g ...

    Text Solution

    |

  18. If f, g: R rarr R are defined by f(x)=x^2+3 x+1, g(x)=2 x-3, find (i) ...

    Text Solution

    |

  19. Let * be a binary operation on N, the set of all natural numbers defin...

    Text Solution

    |

  20. Let A=N xx N and let * be a binary operation on A defined by (a, b)*(...

    Text Solution

    |