. (79 SEPT ME BOARD) A certain manufactured part can be defective because it has one or more out of the three possible defects: insufficient tensile strength, a burr, or a diameter outside of tolerance limit. In a lot of 500 pieces; 19 have a tensile strength defects, 17 have a burr, 11 have an unacceptable diameter, 12 have tensile strength and burr defects, 7 have tensile strength and diameter defects, 5 have burr and diameter defects and 2 have all three defects. How many of the pieces have no defects
Let A be the set of parts that has only insufficient tensile strength, B be the set of parts that has only a burr, C be the set of the parts that has only diameter outside of tolerance limit. Then
"|A\u222aB\u222aC|=|A|+|B|+|C|-|A\u22c2B|-|A\u22c2C|-|C\u22c2B|+|A\u22c2B\u22c2C|=19+17+11-12-7-5+2=25"
We know that 25 details out of 500 has defects, so there is 500 - 25 = 475 pieces without any defects
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