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Prove the following identities a. A‾B‾C‾ + A‾BC‾ + AB‾C‾ + ABC‾ = C‾ b. AB + ABC + A‾ B + AB‾C = B + AC
Ans.
a. LHS = A'B'C' + A'BC' + AB'C' + ABC'= A'C' (B' + B) + AC' (B' + B)= A'C' + AC' [as B'+B = 1]= C' (A' + A)= C' [since A'+A =1]= RHS.Thus Provedb. LHS = AB + ABC + A'B + AB'C
= B + AC= B (A + A') + AC (B + B')= B + AC [as B + B' = A + A' = 1]= B + AC= RHS.Thus Proved
Six machines H1, H2, ..., H6 are linked by two Ethernet switches SW1 and SW2 as given below. Both switches have four ports drawn. The port numbers are as indicated. Suppose the two
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