Skip to content
GATEiit

GATE CSE 2021 Set 1 Q52: Expressions equivalent to the complement of a product of sums

Question

Consider the following Boolean expression.

F=(X+Y+Z)(X‾+Y)(Y‾+Z)F = (X + Y + Z)(\overline{X} + Y)(\overline{Y} + Z)

Which of the following Boolean expressions is/are equivalent to F‾\overline{F} (complement of FF)?

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
Show answer and explanation

Answer: B, C, D (official GATE 2021 final answer key)

Concept used: De Morgan turns the product of sums into a sum of products; then compare minterms or simplify.

First step: F‾=X‾ Y‾ Z‾+XY‾+YZ‾\overline{F} = \overline{X}\,\overline{Y}\,\overline{Z} + X\overline{Y} + Y\overline{Z}; list its minterms and test each option against them.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

More Digital Logic PYQs

PracticePractise Digital Logic questions →Full paperAll GATE CSE 2021 Set 1 questions →