DSSSB TGT CS Mock 02 – Question 126

Question:

In Boolean algebra, what is the dual of the expression \(X + YZ\)?

बूलियन बीजगणित में, व्यंजक \(X + YZ\) का द्वैत (Dual) क्या है?

Options:

  • \(X(Y + Z)\)
  • \(X + (Y + Z)\)
  • \(XY + Z\)
  • \(\overline{X}(\overline{Y} + \overline{Z})\)
  • \(X(Y + Z)\)
  • \(X + (Y + Z)\)
  • \(XY + Z\)
  • \(\overline{X}(\overline{Y} + \overline{Z})\)

Correct Answer: a)

Explanation:

To find the dual of a Boolean expression:
– Interchange OR (+) and AND (\(\cdot\)) operators.
– Interchange 0 and 1.
– Variables remain uncomplemented.
Dual of \(X + Y \cdot Z\) is **\(X(Y + Z)\)** (Option a).

डुअल ज्ञात करने के लिए + और × को आपस में बदला जाता है। अतः \(X + YZ\) का डुअल **\(X(Y + Z)\)** है (विकल्प a)।

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