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Select the Boolean function(s) equivalent to x + yz , where x,y, and z are Boolean variables, and ‘+’ denotes logical OR operation.
- a)x + xz+ xy
- b)x + z+ xy
- c)(x + y)(x+ z)
- d)x + xy+ yz
Correct answer is option 'C,D'. Can you explain this answer?
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Most Upvoted Answer
Select the Boolean function(s) equivalent to x + yz , where x,y, and z...
To find the Boolean function(s) that are equivalent to x yz, we can simplify the expression using Boolean algebra rules.
Given expression: x yz
Using the distributive law of Boolean algebra, we can rewrite the expression as:
x yz = (x y) + (x z)
Therefore, the equivalent Boolean functions are:
A) x xz
B) x z xy
C) (x y)(x z)
D) x xy yz
Now, let's analyze each option to determine if it is equivalent to the given expression:
A) x xz:
This option does not match the simplified expression (x y) + (x z). Therefore, option A is not correct.
B) x z xy:
This option does not match the simplified expression (x y) + (x z). Therefore, option B is not correct.
C) (x y)(x z):
This option matches the simplified expression (x y) + (x z). Therefore, option C is correct.
D) x xy yz:
This option matches the simplified expression (x y) + (x z). Therefore, option D is correct.
Therefore, the correct options are C) (x y)(x z) and D) x xy yz.
Given expression: x yz
Using the distributive law of Boolean algebra, we can rewrite the expression as:
x yz = (x y) + (x z)
Therefore, the equivalent Boolean functions are:
A) x xz
B) x z xy
C) (x y)(x z)
D) x xy yz
Now, let's analyze each option to determine if it is equivalent to the given expression:
A) x xz:
This option does not match the simplified expression (x y) + (x z). Therefore, option A is not correct.
B) x z xy:
This option does not match the simplified expression (x y) + (x z). Therefore, option B is not correct.
C) (x y)(x z):
This option matches the simplified expression (x y) + (x z). Therefore, option C is correct.
D) x xy yz:
This option matches the simplified expression (x y) + (x z). Therefore, option D is correct.
Therefore, the correct options are C) (x y)(x z) and D) x xy yz.
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Community Answer
Select the Boolean function(s) equivalent to x + yz , where x,y, and z...
Given : (x + yz)
Method 1
Choosing from options :
From option (A) :
x + xz+ xy
x(1+ z+ y) (∵ 1+ Anything = 1)
So, option (A) is incorrect.
From option (B) :
x + z+ xy
x(1+ y)+ z (∵ 1+ Anything=1)
x +z
So, option (B) is incorrect.
From option (C) :
(x + y) (x+ z)
x + xz + yx + yz
x(1+ z+ y) (∵ 1+ Anything = 1)
x + yz
So, option (C) is correct.
From option (D) :
x + xy+ yz
x(1+ y)+ yz
x + yz ( ∵ 1+ Anything = 1)
So, option (D) is correct.
Hence, the correct options are (C) & (D).
Method 2
Given : (x + yz) …..(i)
From Boolean algebra, A + BC = ( A + B)( A + C)
So, equation (i) can write as,
x + yz = (x + y)(x + z)
Again from Boolean algebra, A + BC = A + AB + BC
So, equation (i) can write as,
x + yz = x + xy + yz
Hence, the correct options are (C) & (D).
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Select the Boolean function(s) equivalent to x + yz , where x,y, and z are Boolean variables, and ‘+’ denotes logical OR operation.a)x + xz+ xyb)x + z+ xyc)(x + y)(x+ z)d)x + xy+ yzCorrect answer is option 'C,D'. Can you explain this answer?
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