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NAND
F(S)= (a'b)+(bc')+(ac)
F(S)= b·(a'+c)+(ac)
F(S)= (b·(a'+c')+(ac))'
F(S)= ((b·(a'+c'))'·(ac))'
NOT
F(S)= (a'b)+(bc')+(ac)
F(S)= ((b·(a'+c')+(ac))')'
F(S)= (b'+((a'+c')+(a'+c')')')'

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NAND and NOT logic gate truth tables and formulas