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# GATE | Gate IT 2008 | Question 8

• Last Updated : 28 Jun, 2021

Consider the following Boolean function of four variables

f(A, B, C, D) = Σ(2, 3, 6, 7, 8, 9, 10, 11, 12, 13)

The function is
(A) independent of one variable
(B) independent of two variables
(C) independent of three variable
(D) dependent on all the variables

Explanation:

The Karnaugh map solutions of the given function can be obtained in two ways. These are the minimal functions that can be obtained. Thus the functions obtained are independent of variable “D”.

 A’B’ A’B AB AB’ 00 01 11 10 A’B’ 00 1 1 A’B 01 1 1 AB 11 1 1 AB’ 10 1 1 1 1

A’C+AC’+AB’

 A’B’ A’B AB AB’ 00 0 1 11 10 A’B’ 00 1 1 A’B 01 1 1 AB 11 1 1 AB’ 10 1 1 1 1

A’C+AC’+B’C

This solution is contributed by Kriti Kushwaha.

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