x′z′ doesn't imply the expression. Prime implicants of p: x′y, yz′, xz. Symbolic q: ¬(xy′) + ¬(x+y+z) + xz
The expression \(x'z'\) does not imply the expression \(xy'z' + x'y + x'y'z' + x'y'z\). In the given expression \(xy'z' + x'y + x'y'z' + x'y'z\), there's no direct relation or logical implication with \(x'z'\) since the terms do not share the same variables or their complements.
The prime implicants of \(p = xyz + xyz' + x'yz' + x'y'z\) are \(xyz\), \(xy'z'\), and \(x'yz'\).
To reduce the polynomial \(p\) into minimal sum of products, one can use the Karnaugh map or Quine-McCluskey method. Using Karnaugh maps for \(p\), you can group the terms and obtain the minimal sum of products form.
For the circuit \(q = (xy')' + (x+y+z)' + xz\), its contact diagram isn't explicitly provided in text form. However, the symbolic representation of the circuit \(q\) is as follows:
\(q = (xy')' + (x+y+z)' + xz\)
This symbolic representation showcases that the circuit \(q\) comprises a combination of NOT, OR, and AND gates with inputs \(x\), \(y\), and \(z\) connected in the specified manner. To visualize the circuit's connections, a diagram or schematic representation would be needed.
Question : Does the expression x′z′ imply the expression xy′z′+x′y+x′y′z′+x′yz? Give reasons for your answer. Find the prime implicants of p=xyz+xyz′+x′yz′+x′y′z. Also reduce the above polynomial p into minimal sum of products form using Quine-McCluskey method or Karnaugh maps. Draw the contact diagram of the circuit q=(xy′)′+(x+y+z)′+xz. Further, give the symbolic representation of the above circuit q.