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lorgan's laws, what is complementary?
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everything that is not complementary, everything that does not have a bar on top. ex: complementary A U B = left over that which is not A U B
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WHO IS IT? INTERCESSION B AND A? BEING A= 1;2 AND B= 2;3 AND UNIVERSE= 1;2;3;4
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=2...........
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PROVE IT!
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TAKE INTERCESSION A AND B COMPLEMENTARY (EVERYTHING THAT IS NOT (A AND B) = BEING A= 1;2 AND B= 2;3 AND UNIVERSE= 1;2;3;4
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TAKE INTERCESSION A AND B COMPLEMENTARY (EVERYTHING THAT IS NOT (A AND B) = 2) 1;3;4
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JUST TO CHECK A=1;2 COMPLEMENTARY OF A = BEING A= 1;2 AND B= 2;3 AND UNIVERSE= 1;2;3;4
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JUST TO CHECK A=1;2 COMPLEMENTARY OF A=3;4 B=2;3 COMPLEMENTARY OF B= BEING A= 1;2 AND B= 2;3 AND UNIVERSE= 1;2;3;4
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JUST TO CHECK A=1;2 COMPLEMENTARY OF A=3;4 B=2;3 COMPLEMENTARY OF B=1;4
N
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JOIN THE COMPLEMENTS OF A AND B BEING =A=3;4 B=1;4
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N
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UNION B = 1;3;4 RIGHT
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N
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DIFFERENCE BETWEEN SETS A-B? BEING A= 1;2;3;4 B=2;3;7
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N
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=1;4 SCRATCH OUT THE INTERCESSIONS OF A AND B AND O WHAT REMAINING IN A WILL BE THE DIFFERENCE
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B-A? BEING A= 1;2;3;4 B=2;3;7
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=7 SCRATCH OUT THE INTERCESSIONS OF B E A WHAT REMAINING IN B WILL BE THE DIFFERENCE AND LOOK FOR B IN B-A
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OBS.......
N
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PROPRIEDADES DA DIFERENÇA
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A - EMPTY =
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A - EMPTY = A
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N
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A - A =
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A - A = EMPTY
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A - UNIVERSE =
N
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A - UNIVERSE = EMPTY
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N
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A - B = B - A IF AND ONLY IF
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A - B = B - A IF AND ONLY IF A = B
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N
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A - B DIFFERENT B - A IF AND ONLY IF
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A - B = DIFFERENT B - A IF AND ONLY IF A DIFFERENT B
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N
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A - B = EMPTY ->
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A - B = EMPTY -> A = B
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A - B = A -> A INTERCESSION B =
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A - B = A -> A INTERCESSION B = EMPTY
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DIFFERENCE BETWEEN SETS DOESN'T REQUIRE?
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INCLUSION RATIO
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SÓ A......
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1...............
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SÓ B........
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3........
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SÓ C...
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7.........
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SÓ A INTERCESSÃO C
N
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5.......
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N
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SÓ A INTERCESSÃO B
N
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2.......
N
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SÓ B INTERCESSÃO C
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N
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6.......
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N
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A INTERCESSÃO B
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N
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2;4.......
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A INTERCESSÃO C
N
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4;5.....
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B INTERCESSÃO C
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N
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4;6.....
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N
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A INTERCESSÃO B INTERCESSÃO C
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4.........
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A COMPLEMENTAR
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3;6;7.......
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B COMPLEMENTAR
N
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1;5;7...
N
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C COMPLEMENTAR
N
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98
1;2;3...
N
S
