The Boolean expression for the following truth table is ___ x y z f 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1

F=x’yz’ + xy’z + xyz Explanation: Identify the Minterms (where ): Row 3: Row 6: Row 8: Combine the Minterms: Simplify the expression: Take as a common factor from the last two terms: Since (Complement Law):

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NIMCET 2024 Computer PYQ — The Boolean expression for the following truth table is ___ x y z… | Mathem Solvex

A.
F = x’yz’ + xy’z + x’y’z’
B.
F = x’y’z’ + xy’z+xyz’
C.
F=x’yz’ + xy’z + xyz
(Correct Answer)
D.
None of these

Correct Answer:

F=x’yz’ + xy’z + xyz

Explanation

Identify the Minterms (where $f = 1$ ):
- Row 3: $x=0, y=1, z=0 \implies \text{Minterm} = x'yz'$
- Row 6: $x=1, y=0, z=1 \implies \text{Minterm} = xy'z$
- Row 8: $x=1, y=1, z=1 \implies \text{Minterm} = xyz$
Combine the Minterms:

$f = x'yz' + xy'z + xyz$
Simplify the expression:

Take $xz$ as a common factor from the last two terms:

$f = x'yz' + xz(y' + y)$

Since $(y' + y) = 1$ (Complement Law):

$f = x'yz' + xz(1)$

$f = x'yz' + xz$

NIMCET 2024 — Computer PYQ

Choose the correct answer:

Explanation

Explanation