Select the Boolean function(s) equivalent to 𝑥+𝑦𝑧, where 𝑥,𝑦, and 𝑧 are Boolean variables, and + denotes logical OR operation

 

Select the Boolean function(s) equivalent to 𝑥+𝑦𝑧, where 𝑥,𝑦, and 𝑧 are Boolean variables, and + denotes logical OR operation. 

 (A) 𝑥+𝑧+𝑥𝑦 

 (B) (𝑥+𝑦)(𝑥+𝑧) 

 (C) 𝑥+𝑥𝑦+𝑦𝑧 

 (D) 𝑥+𝑥𝑧+𝑥𝑦 

Answers: Options B and C

Solution:

Option B: (𝑥+𝑦)(𝑥+𝑧) = x.x + x.z + x.y + yz = x(1+y+z) + yz =  x+yz

Option C: 𝑥+𝑥𝑦+𝑦𝑧 = x(1+y)+yz = x+yz

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