The two construction statements are correct and the two function-implementation statements are not — option 3.

(C) — building a 64-input MUX from 8-input MUXs. Two stages are needed:

The six select lines of the 64-input MUX split three-and-three between the stages, and \(8\times8=64\) inputs are covered exactly.

(D) — the demultiplexer is the mirror image. One 3-to-8 DEMUX in the first stage steers the incoming data to one of eight second-stage devices, and each of those eight fans out to eight outputs, giving \(8\times8=64\) outputs from nine devices. The counts are identical because a demultiplexer is a multiplexer with the signal flow reversed.

(B) is false on a straightforward count. A 3-line to 8-line demultiplexer has only three select inputs, so it can generate the eight minterms of three variables. Four variables need sixteen minterms and therefore a 4-to-16 device. The statement is short by a factor of two.

(A) is false as written, and this is worth separating carefully. There is a true statement close to it: a \(2^{n}\)-to-1 multiplexer can implement any function of n + 1 variables, so an 8-input MUX can implement any 4-variable function — wire three variables to the select lines and the fourth, its complement, 0 or 1 to each data input, following the Shannon expansion. But statement (A) reverses this, saying the MUX can be implemented using a function, which is not a meaningful claim about hardware. Since option 3 is the only choice excluding both (A) and (B), the reversal is evidently intended.

The general rule for cascading is worth carrying away: to build a \(2^{m}\)-input multiplexer from \(2^{k}\)-input ones takes

\(\dfrac{2^{m}-1}{2^{k}-1}\ \text{devices}\)

which for m = 6 and k = 3 gives \(63/7=9\) — confirming both (C) and (D) in one line.

Hence, the correct statements are (C) and (D).