Home
Class 12
MATHS
Prove that f:X rarr Y is injective iff ...

Prove that `f:X rarr Y` is injective iff for all `subsets A,B of X,f(A nn B ) = f(A) nn f(B)`.

Promotional Banner

Topper's Solved these Questions

  • PREVIOUS YEAR QUESTION 2018

    USHA PUBLICATION|Exercise PREVIOUS YEAR QUESTION |48 Videos

  • PREVIOUS YEAR QUESTION 2020

    USHA PUBLICATION|Exercise PREVIOUS YEAR QUESTION |46 Videos

Similar Questions

Explore conceptually related problems

Prove that f:X to Y is injective iff for all subsets A, B of X, f (A cap B) =f(A) cap f(B) .

Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B)) =B.

Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A sube X .

Prove that f: X rarr Y is surjective iff for all A sube X,(f(A))' sube f(A') , where A' denotes the complement of A in X.

Prove that for any f:X rarr Y , f o id_x = f =id_Y of.

Prove that A nn(B uu C) =(A nn B) uu (A nn C)

Prove that f(x)=|x| is not differetiable at x=0

Using the definition, prove that the function f: A rarr B is invertible, if and only if f is both one-one and onto.

Let f be defined by f (x)=2x + 1 for all xinR . Show that f is bijective and determine the inverse of f. Find f^(-1)(0),f^(-1)(2) and f^(-1)(-1) .

USHA PUBLICATION-PREVIOUS YEAR QUESTION 2019-PREVIOUS YEAR QUESTION
  1. Obtain the general solution of the following differential equations. (...

    Text Solution

    |

  2. Integrate the following int[(2x+1)/sqrt(x^2+10x+29)]dx

    Text Solution

    |

  3. Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2.

    Text Solution

    |

  4. Find the equation of a plane which is at a distance 3 units from the o...

    Text Solution

    |

  5. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

    Text Solution

    |

  6. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

    Text Solution

    |

  7. Find the unit vector in the direction of the vector vecr1-vecr2, where...

    Text Solution

    |

  8. Find the inverse of the following matrices using elementary transforma...

    Text Solution

    |

  9. Out of the adult population in a village 50% are farmers, 30% do busin...

    Text Solution

    |

  10. Examining consistency and solvability, solve the following equation by...

    Text Solution

    |

  11. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

    Text Solution

    |

  12. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

    Text Solution

    |

  13. Evaluate the following integrals int(dx)/(2cos^2x+3cosx)

    Text Solution

    |

  14. Solve y^(2)+x^(2)dy/dx=xydy/dx.

    Text Solution

    |

  15. Determine the area common to the parabola y^2=x and the circle x^2+y^2...

    Text Solution

    |

  16. Find the distance of the point (1,-1,-10) from the line (x-4)/1=(y+3)/...

    Text Solution

    |

  17. Show by vector method that the four points (6, 2, -1), (2, -1, 3), (-1...

    Text Solution

    |

  18. Prove that f:X rarr Y is injective iff for all subsets A,B of X,f(A n...

    Text Solution

    |

  19. Maximize:Z=10x1+12x2+8x3 "Subject to": x1+2x2 le 30 5x1 -7x3 ge 12 x1+...

    Text Solution

    |

  20. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

    Text Solution

    |