Gate applied test series 2022

Question

Given 2 functions X and Y, we can say function X covers function Y iff all the minterms of function Y are covered by function X ( i.e X should be superset of Y).  Let Y be a function of 3 ternary variables, Y(a,b) having 15 minterms. The  number of functions covering Y are ______

Comments

Ans is 2 ??

Answer 1

Answer will be 2

The question asks- how many super sets can be generated such that 15 minterms of Y are covered. 

total number of logical expressions created from (a,b) = 4^n  =  4^2 = 16

Since 15 are the elements of Y for which X is super set X, hence X can either have 15 or 16 elements itself. Answer is 2

Comments

Number of logical expression created would be 3^n as it is ternary variable