A function of Boolean variables x,y\:and\:z is expressed in terms of the min-term as F (x,y,z) \: = \:\sum \: (1,2,5,6,7). Which one of the product of sums given below is equal to F(x,y,z)

Correct Answer is : (x+y+z)(x+y¯+z¯)(x¯+y+z)

(x^{¯} + \:y^{¯} + \:z^{¯}) (x^{¯} + \:y\: + \:z) (x\: + \:y^{¯} + \:z^{¯})

(x\: + \:y\: + \:z) (x\: + \:y^{¯} + \:z^{¯}) (x^{¯} + \:y\: + \:z)

(x^{¯} + \:y^{¯} + \:z) (x^{¯} + \:y\: + \:z^{¯}) (x\: + \:y^{¯} + \:z) (x\: + \:y\: + \:z)

(x\: + \:y\: + \:z^{¯}) (x^{¯} + \:y\: + \:z) (x^{¯} + \:y\: + \:z^{¯}) (x^{¯} + \:y^{¯} + \:z) (x^{¯} + \:y^{¯} + \:z^{¯})

GATE Electronics and Communications (EC) 2015 Shift 2 Solved Paper

Question : 46 of 65

Marks: +1, -0

A function of Boolean variables

x,y\:and\:z

is expressed in terms of the min-term as

F (x,y,z) \: = \:Σ \: (1,2,5,6,7)

. Which one of the product of sums given below is equal to F(x,y,z)

$(x↖{¯} + \:y↖{¯} + \:z↖{¯}) (x↖{¯} + \:y\: + \:z) (x\: + \:y↖{¯} + \:z↖{¯})$
$(x\: + \:y\: + \:z) (x\: + \:y↖{¯} + \:z↖{¯}) (x↖{¯} + \:y\: + \:z)$
$(x↖{¯} + \:y↖{¯} + \:z) (x↖{¯} + \:y\: + \:z↖{¯}) (x\: + \:y↖{¯} + \:z) (x\: + \:y\: + \:z)$
$(x\: + \:y\: + \:z↖{¯}) (x↖{¯} + \:y\: + \:z) (x↖{¯} + \:y\: + \:z↖{¯}) (x↖{¯} + \:y↖{¯} + \:z) (x↖{¯} + \:y↖{¯} + \:z↖{¯})$

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