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When simplified with boolean algebra, the expression (x + y)(x + z) simplies to :
- a)x(1 + yz)
- b)x + yz
- c)x
- d)x + x(y+z)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
When simplified with boolean algebra, the expression (x + y)(x + z) si...
The correct answer is: x + yz
Most Upvoted Answer
When simplified with boolean algebra, the expression (x + y)(x + z) si...
(x+y)(x+z)
= x.x + x.z + x.y + y.z
= x.(1 + y +z) + y.z
= x + y.z
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When simplified with boolean algebra, the expression (x + y)(x + z) si...
Simplifying the expression (x y)(x z) using Boolean algebra:
Step 1: Expand the expression using the distributive property of multiplication over addition.
(x y)(x z) = x(x z) + y(x z)
Step 2: Simplify each term separately.
Simplifying x(x z):
Using the distributive property, x(x z) can be expanded as x * x + x * z.
x * x is equal to x, and x * z is equal to xz.
Therefore, x(x z) simplifies to x + xz.
Simplifying y(x z):
Using the distributive property, y(x z) can be expanded as y * x + y * z.
y * x is equal to xy, and y * z is equal to yz.
Therefore, y(x z) simplifies to xy + yz.
Step 3: Combine the simplified terms.
x + xz + xy + yz
Step 4: Group the terms with common factors.
(x + xy) + (xz + yz)
Step 5: Factor out the common factor from each group.
x(1 + y) + z(x + y)
Step 6: Simplify the expression further.
Since (1 + y) is always equal to 1 (since y can only be 0 or 1), we can simplify x(1 + y) to just x.
Similarly, we can simplify z(x + y) to just zx.
The simplified expression is:
x + zx
Since zx is equivalent to xz, the final simplified expression is:
x + xz
Therefore, the correct answer is option B: x + xz.
Step 1: Expand the expression using the distributive property of multiplication over addition.
(x y)(x z) = x(x z) + y(x z)
Step 2: Simplify each term separately.
Simplifying x(x z):
Using the distributive property, x(x z) can be expanded as x * x + x * z.
x * x is equal to x, and x * z is equal to xz.
Therefore, x(x z) simplifies to x + xz.
Simplifying y(x z):
Using the distributive property, y(x z) can be expanded as y * x + y * z.
y * x is equal to xy, and y * z is equal to yz.
Therefore, y(x z) simplifies to xy + yz.
Step 3: Combine the simplified terms.
x + xz + xy + yz
Step 4: Group the terms with common factors.
(x + xy) + (xz + yz)
Step 5: Factor out the common factor from each group.
x(1 + y) + z(x + y)
Step 6: Simplify the expression further.
Since (1 + y) is always equal to 1 (since y can only be 0 or 1), we can simplify x(1 + y) to just x.
Similarly, we can simplify z(x + y) to just zx.
The simplified expression is:
x + zx
Since zx is equivalent to xz, the final simplified expression is:
x + xz
Therefore, the correct answer is option B: x + xz.
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When simplified with boolean algebra, the expression (x + y)(x + z) simplies to :a)x(1 + yz)b)x + yzc)xd)x + x(y+z)Correct answer is option 'B'. Can you explain this answer?
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