Question

What does the Distributive property signify?

(a) The sum of signals in both the sides in any number must be equal

(b) The responses must be equal in any side of an LTI system

(c) The sum of two inputs must be equal to responses to these signals

(d) The Multiplication of two signals in the inputs side is equal to multiplication of the responses

The question was asked in an international level competition.

This interesting question is from Properties of LTI Systems topic in division Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

Correct choice is (c) The sum of two inputs must be equal to responses to these signals

Easiest explanation: The sum of two inputs must be equal to responses to these signals individually.

x[n]*(h1[n]+h2[n])=x[n]*h1[n]+x[n]*h2[n], with x[n] being the input and h1[n] and h2[2] being the impulse responses.