Problem Statement:

A four-variable logic function that is equal to 1 if any three or all four of its variables are equal to 1 is called a​

majority function. Design a minimum-cost SOP circuit that implements the majority function.

The function I got is as follows,

\(x_{1}x_{2} + x_{3}x_{4}\)

They list the answer as something with more gates but I can't see how this one doesn't work just fine.

Are they wrong, or am I just crazy?​

 

Create a truth table for the problem statement and you'll find your function doesn't satisfy it.

For example, your function outputs a 1 if x1 and x2 are 1.
That isn't a majority since only 2 of the 4 inputs are 1.
Similarly this happens when x3 and x4 are 1.