\(x\) | \(y\) | \(z\) | \(f(x,y,z)\) | |

0 | 0 | 0 | 0 | |

0 | 0 | 1 | 0 | |

0 | 1 | 0 | 0 | |

0 | 1 | 1 | 1 | |

1 | 0 | 0 | 0 | |

1 | 0 | 1 | 1 | |

1 | 1 | 0 | 1 | |

1 | 1 | 1 | 0 |

What is the \(\text{minimum}\) number of \(\text{AND}\), \(\text{OR}\) and \(\text{NOT}\) gates used to implement the \(\text{Boolean Function} \) \(f(x,y,z)\) described above?

**Details and assumptions:**

You cannot use gates other than mentioned ones.

You are free to use either the two-input or three-input or four-input logic gates or so whereas \(\text{NOT}\) gate is always a uni-input gate.

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