## Relations-and-Functions

Question 1 |

The number of onto function (surjective function) from set X = {1, 2, 3, 4} to set Y = {a, b, c} is ______.

36 | |

37 | |

38 | |

39 |

Question 1 Explanation:

Number of onto function from set X to set Y with |X| = m, |Y| = n is

m = 4, n = 3 ⇒ number of onto function is

m = 4, n = 3 ⇒ number of onto function is

Question 2 |

Let S denote the set of all functions f:{0,1}

^{4 }→ {0,1}. Denote by N the number of functions from S to the set {0,1}. The value of log_{2 }log_{2}N is ______.16 | |

17 | |

18 | |

19 |

Question 2 Explanation:

The number of functions from A to B where size of A=|A| and size of B=|B| is |B|

{0,1}

|S|=2

N=2

loglogN=loglog2

^{|A|}{0,1}

^{4}={0,1}×{0,1}×{0,1}×{0,1}=16|S|=2

^{16}N=2

^{|S|}loglogN=loglog2

^{|S|}=log |S| =log2^{16}=16
There are 2 questions to complete.